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Drozd. “Morita Theory for Non-Commutative Noetherian Schemes.” Advances in Mathematics 399 (2022). https://doi.org/10.1016/j.aim.2022.108273.","bibtex":"@article{Burban_Drozd_2022, title={Morita theory for non-commutative noetherian schemes}, volume={399}, DOI={10.1016/j.aim.2022.108273}, number={108273}, journal={Advances in Mathematics}, author={Burban, Igor and Drozd, Yu.}, year={2022} }","mla":"Burban, Igor, and Yu. Drozd. “Morita Theory for Non-Commutative Noetherian Schemes.” Advances in Mathematics, vol. 399, 108273, 2022, doi:10.1016/j.aim.2022.108273."},"language":[{"iso":"eng"}],"title":"Morita theory for non-commutative noetherian schemes","user_id":"49063","abstract":[{"text":"In this paper, we study equivalences between the categories of quasi–coherent sheaves on non–commutative noetherian schemes. In particular, we give a new proof of Căldăraru's conjecture about Morita equivalences of Azumaya algebras on noetherian schemes. Moreover, we derive necessary and sufficient condition for two reduced non–commutative curves to be Morita equivalent.","lang":"eng"}],"volume":399,"publication_status":"published","date_created":"2023-05-02T18:34:25Z","status":"public","department":[{"_id":"602"}],"publication":"Advances in Mathematics","author":[{"id":"72064","last_name":"Burban","full_name":"Burban, Igor","first_name":"Igor"},{"last_name":"Drozd","first_name":"Yu.","full_name":"Drozd, Yu."}]},{"title":"A classification of polyharmonic Maa forms via quiver representations","user_id":"49063","publication_status":"published","status":"public","date_created":"2023-05-07T00:54:50Z","author":[{"full_name":"Burban, Igor","first_name":"Igor","id":"72064","last_name":"Burban"},{"first_name":"C.","full_name":"Alfes-Neumann, C.","last_name":"Alfes-Neumann"},{"last_name":"Raum","full_name":"Raum, M.","first_name":"M."}],"department":[{"_id":"602"}],"_id":"44537","date_updated":"2023-05-07T01:37:00Z","year":"2022","citation":{"bibtex":"@article{Burban_Alfes-Neumann_Raum_2022, title={A classification of polyharmonic Maa forms via quiver representations}, author={Burban, Igor and Alfes-Neumann, C. and Raum, M.}, year={2022} }","mla":"Burban, Igor, et al. A Classification of Polyharmonic Maa Forms via Quiver Representations. 2022.","chicago":"Burban, Igor, C. Alfes-Neumann, and M. Raum. “A Classification of Polyharmonic Maa Forms via Quiver Representations,” 2022.","apa":"Burban, I., Alfes-Neumann, C., & Raum, M. (2022). A classification of polyharmonic Maa forms via quiver representations.","ama":"Burban I, Alfes-Neumann C, Raum M. A classification of polyharmonic Maa forms via quiver representations. Published online 2022.","ieee":"I. Burban, C. Alfes-Neumann, and M. Raum, “A classification of polyharmonic Maa forms via quiver representations.” 2022.","short":"I. Burban, C. Alfes-Neumann, M. 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Peruzzi. “On Elliptic Solutions of the Associative Yang-Baxter Equation.” Journal of Geometry and Physics 176 (2022).","apa":"Burban, I., & Peruzzi, A. (2022). On elliptic solutions of the associative Yang-Baxter equation. Journal of Geometry and Physics, 176, Article 104499.","ama":"Burban I, Peruzzi A. On elliptic solutions of the associative Yang-Baxter equation. Journal of Geometry and Physics. 2022;176.","bibtex":"@article{Burban_Peruzzi_2022, title={On elliptic solutions of the associative Yang-Baxter equation}, volume={176}, number={104499}, journal={Journal of Geometry and Physics}, author={Burban, Igor and Peruzzi, A.}, year={2022} }","mla":"Burban, Igor, and A. Peruzzi. “On Elliptic Solutions of the Associative Yang-Baxter Equation.” Journal of Geometry and Physics, vol. 176, 104499, 2022."},"type":"journal_article","language":[{"iso":"eng"}],"article_number":"104499","intvolume":" 176","_id":"44327","date_updated":"2023-05-07T01:41:35Z"},{"type":"journal_article","year":"2021","citation":{"apa":"Burban, I., & Abedin, R. (2021). Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation. Communications in Mathematical Physics, 387(2), 1051–1109. https://doi.org/10.1007/s00220-021-04188-7","ama":"Burban I, Abedin R. Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation. Communications in Mathematical Physics. 2021;387(2):1051–1109. doi:10.1007/s00220-021-04188-7","chicago":"Burban, Igor, and R. Abedin. “Algebraic Geometry of Lie Bialgebras Defined by Solutions of the Classical Yang-Baxter Equation.” Communications in Mathematical Physics 387, no. 2 (2021): 1051–1109. https://doi.org/10.1007/s00220-021-04188-7.","mla":"Burban, Igor, and R. Abedin. “Algebraic Geometry of Lie Bialgebras Defined by Solutions of the Classical Yang-Baxter Equation.” Communications in Mathematical Physics, vol. 387, no. 2, 2021, pp. 1051–1109, doi:10.1007/s00220-021-04188-7.","bibtex":"@article{Burban_Abedin_2021, title={Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation}, volume={387}, DOI={10.1007/s00220-021-04188-7}, number={2}, journal={Communications in Mathematical Physics}, author={Burban, Igor and Abedin, R.}, year={2021}, pages={1051–1109} }","short":"I. Burban, R. Abedin, Communications in Mathematical Physics 387 (2021) 1051–1109.","ieee":"I. Burban and R. Abedin, “Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation,” Communications in Mathematical Physics, vol. 387, no. 2, pp. 1051–1109, 2021, doi: 10.1007/s00220-021-04188-7."},"page":"1051–1109","language":[{"iso":"eng"}],"intvolume":" 387","_id":"44329","date_updated":"2023-05-07T01:35:11Z","doi":"10.1007/s00220-021-04188-7","issue":"2","author":[{"first_name":"Igor","full_name":"Burban, Igor","last_name":"Burban","id":"72064"},{"first_name":"R.","full_name":"Abedin, R.","last_name":"Abedin"}],"department":[{"_id":"602"}],"publication":"Communications in Mathematical Physics","publication_status":"published","volume":387,"status":"public","date_created":"2023-05-02T18:36:54Z","abstract":[{"lang":"eng","text":"This paper is devoted to algebro-geometric study of infinite dimensional Lie bialgebras, which arise from solutions of the classical Yang–Baxter equation. We regard trigonometric solutions of this equation as twists of the standard Lie bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding theory of Manin triples, putting it into an algebro-geometric context. As a consequence of this approach, we prove that any trigonometric solution of the classical Yang–Baxter equation arises from an appropriate algebro-geometric datum. The developed theory is illustrated by some concrete examples."}],"title":"Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation","user_id":"49063"},{"issue":"4","doi":"10.1112/plms.12341","_id":"44331","intvolume":" 121","date_updated":"2023-05-07T01:30:54Z","language":[{"iso":"eng"}],"page":"1033–1082","citation":{"chicago":"Burban, Igor, and A. Zheglov. “Cohen-Macaulay Modules over the Algebra of Planar Quasi-Invariants and Calogero-Moser Systems.” Proceedings of the London Mathematical Society 121, no. 4 (2020): 1033–1082. https://doi.org/10.1112/plms.12341.","ama":"Burban I, Zheglov A. Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems. Proceedings of the London Mathematical Society. 2020;121(4):1033–1082. doi:10.1112/plms.12341","apa":"Burban, I., & Zheglov, A. (2020). Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems. Proceedings of the London Mathematical Society, 121(4), 1033–1082. https://doi.org/10.1112/plms.12341","mla":"Burban, Igor, and A. Zheglov. “Cohen-Macaulay Modules over the Algebra of Planar Quasi-Invariants and Calogero-Moser Systems.” Proceedings of the London Mathematical Society, vol. 121, no. 4, 2020, pp. 1033–1082, doi:10.1112/plms.12341.","bibtex":"@article{Burban_Zheglov_2020, title={Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems}, volume={121}, DOI={10.1112/plms.12341}, number={4}, journal={Proceedings of the London Mathematical Society}, author={Burban, Igor and Zheglov, A.}, year={2020}, pages={1033–1082} }","short":"I. Burban, A. Zheglov, Proceedings of the London Mathematical Society 121 (2020) 1033–1082.","ieee":"I. Burban and A. Zheglov, “Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems,” Proceedings of the London Mathematical Society, vol. 121, no. 4, pp. 1033–1082, 2020, doi: 10.1112/plms.12341."},"type":"journal_article","year":"2020","user_id":"49063","title":"Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems","abstract":[{"text":"In this paper, we study properties of the algebras of planar quasi-invariants. These algebras are Cohen–Macaulay and Gorenstein in codimension one. Using the technique of matrix problems, we classify all Cohen–Macaulay modules of rank one over them and determine their Picard groups. In terms of this classification, we describe the spectral modules of the planar rational Calogero–Moser systems. Finally, we elaborate the theory of the algebraic inverse scattering method, providing explicit computations of some ‘isospectral deformations’ of the planar rational Calogero–Moser system in the case of the split rational potential.","lang":"eng"}],"date_created":"2023-05-02T18:47:19Z","status":"public","publication_status":"published","volume":121,"department":[{"_id":"602"}],"publication":"Proceedings of the London Mathematical Society","author":[{"last_name":"Burban","id":"72064","first_name":"Igor","full_name":"Burban, Igor"},{"last_name":"Zheglov","first_name":"A.","full_name":"Zheglov, A."}]},{"title":"Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation","user_id":"49063","abstract":[{"text":"This work deals with an algebro–geometric theory of solutions of the classical Yang–Baxter equation based on torsion free coherent sheaves of Lie algebras on Weierstraß cubic curves.","lang":"eng"}],"volume":364,"publication_status":"published","date_created":"2023-05-02T18:50:35Z","status":"public","department":[{"_id":"602"}],"publication":"Communications in Mathematical Physics","author":[{"full_name":"Burban, Igor","first_name":"Igor","id":"72064","last_name":"Burban"},{"last_name":"Galinat","full_name":"Galinat, L.","first_name":"L."}],"doi":"10.1007/s00220-018-3172-2","issue":"1","intvolume":" 364","_id":"44333","date_updated":"2023-05-07T01:34:43Z","page":"123–169","citation":{"ieee":"I. Burban and L. Galinat, “Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation,” Communications in Mathematical Physics, vol. 364, no. 1, pp. 123–169, 2018, doi: 10.1007/s00220-018-3172-2.","short":"I. Burban, L. Galinat, Communications in Mathematical Physics 364 (2018) 123–169.","bibtex":"@article{Burban_Galinat_2018, title={Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation}, volume={364}, DOI={10.1007/s00220-018-3172-2}, number={1}, journal={Communications in Mathematical Physics}, author={Burban, Igor and Galinat, L.}, year={2018}, pages={123–169} }","mla":"Burban, Igor, and L. Galinat. “Torsion Free Sheaves on Weierstraß Cubic Curves and the Classical Yang-Baxter Equation.” Communications in Mathematical Physics, vol. 364, no. 1, 2018, pp. 123–169, doi:10.1007/s00220-018-3172-2.","ama":"Burban I, Galinat L. Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation. 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Galinat. “Torsion Free Sheaves on Weierstraß Cubic Curves and the Classical Yang-Baxter Equation.” Communications in Mathematical Physics 364, no. 1 (2018): 123–169. https://doi.org/10.1007/s00220-018-3172-2."},"type":"journal_article","year":"2018","language":[{"iso":"eng"}]},{"title":"Non-commutative nodal curves and derived tame algebras","user_id":"49063","publication_status":"published","date_created":"2023-05-07T00:56:31Z","status":"public","department":[{"_id":"602"}],"author":[{"last_name":"Burban","id":"72064","first_name":"Igor","full_name":"Burban, Igor"},{"last_name":"Drozd","full_name":"Drozd, Yu.","first_name":"Yu."}],"date_updated":"2023-05-07T01:36:42Z","_id":"44538","citation":{"mla":"Burban, Igor, and Yu. Drozd. Non-Commutative Nodal Curves and Derived Tame Algebras. 2018.","bibtex":"@article{Burban_Drozd_2018, title={Non-commutative nodal curves and derived tame algebras}, author={Burban, Igor and Drozd, Yu.}, year={2018} }","chicago":"Burban, Igor, and Yu. Drozd. “Non-Commutative Nodal Curves and Derived Tame Algebras,” 2018.","ama":"Burban I, Drozd Yu. Non-commutative nodal curves and derived tame algebras. Published online 2018.","apa":"Burban, I., & Drozd, Yu. (2018). Non-commutative nodal curves and derived tame algebras.","ieee":"I. Burban and Yu. Drozd, “Non-commutative nodal curves and derived tame algebras.” 2018.","short":"I. Burban, Yu. Drozd, (2018)."},"year":"2018","type":"preprint","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1805.05174"}]},{"citation":{"apa":"Burban, I., & Zheglov, A. (2018). Fourier-Mukai transform on Weierstraß cubics and commuting differential operators. International Journal of Mathematics, 29(10), Article 1850064- 46 pp.","ama":"Burban I, Zheglov A. Fourier-Mukai transform on Weierstraß cubics and commuting differential operators. International Journal of Mathematics. 2018;29(10).","chicago":"Burban, Igor, and A. Zheglov. “Fourier-Mukai Transform on Weierstraß Cubics and Commuting Differential Operators.” International Journal of Mathematics 29, no. 10 (2018).","bibtex":"@article{Burban_Zheglov_2018, title={Fourier-Mukai transform on Weierstraß cubics and commuting differential operators}, volume={29}, number={101850064–46 pp}, journal={International Journal of Mathematics}, author={Burban, Igor and Zheglov, A.}, year={2018} }","mla":"Burban, Igor, and A. Zheglov. “Fourier-Mukai Transform on Weierstraß Cubics and Commuting Differential Operators.” International Journal of Mathematics, vol. 29, no. 10, 1850064-46 pp, 2018.","short":"I. Burban, A. Zheglov, International Journal of Mathematics 29 (2018).","ieee":"I. Burban and A. 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Drozd. Maximal Cohen-Macaulay Modules over Non-Isolated Surface Singularities and Matrix Problems. 1178th ed. Vol. 248. Memoirs of the American Mathematical Society, 2017. https://doi.org/10.1090/memo/1178.","apa":"Burban, I., & Drozd, Yu. (2017). Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems (1178th ed., Vol. 248). https://doi.org/10.1090/memo/1178","ama":"Burban I, Drozd Yu. Maximal Cohen-Macaulay Modules over Non-Isolated Surface Singularities and Matrix Problems. Vol 248. 1178th ed.; 2017. doi:10.1090/memo/1178","mla":"Burban, Igor, and Yu. Drozd. Maximal Cohen-Macaulay Modules over Non-Isolated Surface Singularities and Matrix Problems. 1178th ed., vol. 248, 2017, doi:10.1090/memo/1178.","bibtex":"@book{Burban_Drozd_2017, edition={1178}, series={Memoirs of the American Mathematical Society}, title={Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems}, volume={248}, DOI={10.1090/memo/1178}, author={Burban, Igor and Drozd, Yu.}, year={2017}, collection={Memoirs of the American Mathematical Society} }","short":"I. Burban, Yu. Drozd, Maximal Cohen-Macaulay Modules over Non-Isolated Surface Singularities and Matrix Problems, 1178th ed., 2017.","ieee":"I. Burban and Yu. Drozd, Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems, 1178th ed., vol. 248. 2017."},"year":"2017","series_title":"Memoirs of the American Mathematical Society","user_id":"49063","title":"Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems","extern":"1","status":"public","date_created":"2023-05-02T18:59:05Z","publication_identifier":{"isbn":["978-1-4704-2537-1"]},"publication_status":"published","volume":248,"edition":"1178","author":[{"last_name":"Burban","id":"72064","first_name":"Igor","full_name":"Burban, Igor"},{"first_name":"Yu.","full_name":"Drozd, Yu.","last_name":"Drozd"}],"department":[{"_id":"602"}]},{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1706.08358"}],"type":"preprint","citation":{"ieee":"I. Burban and Yu. Drozd, “On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems.” 2017.","short":"I. Burban, Yu. Drozd, (2017).","bibtex":"@article{Burban_Drozd_2017, title={On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems}, author={Burban, Igor and Drozd, Yu.}, year={2017} }","mla":"Burban, Igor, and Yu. Drozd. On the Derived Categories of Gentle and Skew-Gentle Algebras: Homological Algebra and Matrix Problems. 2017.","chicago":"Burban, Igor, and Yu. Drozd. “On the Derived Categories of Gentle and Skew-Gentle Algebras: Homological Algebra and Matrix Problems,” 2017.","apa":"Burban, I., & Drozd, Yu. (2017). On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems.","ama":"Burban I, Drozd Yu. On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems. Published online 2017."},"year":"2017","language":[{"iso":"eng"}],"date_updated":"2023-05-07T01:36:54Z","_id":"44539","author":[{"id":"72064","last_name":"Burban","full_name":"Burban, Igor","first_name":"Igor"},{"last_name":"Drozd","first_name":"Yu.","full_name":"Drozd, Yu."}],"department":[{"_id":"602"}],"publication_status":"published","status":"public","date_created":"2023-05-07T00:57:34Z","extern":"1","title":"On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems","user_id":"49063"},{"author":[{"id":"72064","last_name":"Burban","full_name":"Burban, Igor","first_name":"Igor"},{"first_name":"L.","full_name":"Galinat, L.","last_name":"Galinat"}],"department":[{"_id":"602"}],"publication":"Journal of Physics A: Mathematical and Theoretical","publication_status":"published","volume":50,"status":"public","date_created":"2023-05-02T18:51:44Z","extern":"1","title":"Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions of CYBE","user_id":"49063","citation":{"short":"I. Burban, L. Galinat, Journal of Physics A: Mathematical and Theoretical 50 (2017).","ieee":"I. Burban and L. Galinat, “Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions of CYBE,” Journal of Physics A: Mathematical and Theoretical, vol. 50, Art. no. 454002, 2017.","chicago":"Burban, Igor, and L. Galinat. “Simple Vector Bundles on a Nodal Weierstraß Cubic and Quasi-Trigonometric Solutions of CYBE.” Journal of Physics A: Mathematical and Theoretical 50 (2017).","apa":"Burban, I., & Galinat, L. (2017). Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions of CYBE. Journal of Physics A: Mathematical and Theoretical, 50, Article 454002.","ama":"Burban I, Galinat L. Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions of CYBE. Journal of Physics A: Mathematical and Theoretical. 2017;50.","bibtex":"@article{Burban_Galinat_2017, title={Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions of CYBE}, volume={50}, number={454002}, journal={Journal of Physics A: Mathematical and Theoretical}, author={Burban, Igor and Galinat, L.}, year={2017} }","mla":"Burban, Igor, and L. Galinat. “Simple Vector Bundles on a Nodal Weierstraß Cubic and Quasi-Trigonometric Solutions of CYBE.” Journal of Physics A: Mathematical and Theoretical, vol. 50, 454002, 2017."},"year":"2017","type":"journal_article","language":[{"iso":"eng"}],"_id":"44334","intvolume":" 50","date_updated":"2023-05-07T01:40:53Z","article_number":"454002"},{"author":[{"id":"72064","last_name":"Burban","full_name":"Burban, Igor","first_name":"Igor"},{"full_name":"Drozd, Yu.","first_name":"Yu.","last_name":"Drozd"},{"full_name":"Gavran, V.","first_name":"V.","last_name":"Gavran"}],"publication":"European Journal of Mathematics","department":[{"_id":"602"}],"status":"public","date_created":"2023-05-02T18:53:20Z","volume":3,"publication_status":"published","extern":"1","user_id":"49063","title":"Minors of non-commutative schemes","language":[{"iso":"eng"}],"citation":{"apa":"Burban, I., Drozd, Yu., & Gavran, V. (2017). Minors of non-commutative schemes. European Journal of Mathematics, 3(2), 311–341.","ama":"Burban I, Drozd Yu, Gavran V. Minors of non-commutative schemes. European Journal of Mathematics. 2017;3(2):311–341.","chicago":"Burban, Igor, Yu. Drozd, and V. Gavran. “Minors of Non-Commutative Schemes.” European Journal of Mathematics 3, no. 2 (2017): 311–341.","mla":"Burban, Igor, et al. “Minors of Non-Commutative Schemes.” European Journal of Mathematics, vol. 3, no. 2, 2017, pp. 311–341.","bibtex":"@article{Burban_Drozd_Gavran_2017, title={Minors of non-commutative schemes}, volume={3}, number={2}, journal={European Journal of Mathematics}, author={Burban, Igor and Drozd, Yu. and Gavran, V.}, year={2017}, pages={311–341} }","short":"I. Burban, Yu. Drozd, V. Gavran, European Journal of Mathematics 3 (2017) 311–341.","ieee":"I. Burban, Yu. Drozd, and V. 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