{"title":"Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation","publication":"Communications in Mathematical Physics","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."}],"page":"1051–1109","intvolume":"       387","language":[{"iso":"eng"}],"issue":"2","date_updated":"2023-05-07T01:35:11Z","citation":{"mla":"Burban, Igor, and R. Abedin. “Algebraic Geometry of Lie Bialgebras Defined by Solutions of the Classical Yang-Baxter Equation.” <i>Communications in Mathematical Physics</i>, vol. 387, no. 2, 2021, pp. 1051–1109, doi:<a href=\"https://doi.org/10.1007/s00220-021-04188-7\">10.1007/s00220-021-04188-7</a>.","chicago":"Burban, Igor, and R. Abedin. “Algebraic Geometry of Lie Bialgebras Defined by Solutions of the Classical Yang-Baxter Equation.” <i>Communications in Mathematical Physics</i> 387, no. 2 (2021): 1051–1109. <a href=\"https://doi.org/10.1007/s00220-021-04188-7\">https://doi.org/10.1007/s00220-021-04188-7</a>.","apa":"Burban, I., &#38; Abedin, R. (2021). Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation. <i>Communications in Mathematical Physics</i>, <i>387</i>(2), 1051–1109. <a href=\"https://doi.org/10.1007/s00220-021-04188-7\">https://doi.org/10.1007/s00220-021-04188-7</a>","short":"I. Burban, R. Abedin, Communications in Mathematical Physics 387 (2021) 1051–1109.","ama":"Burban I, Abedin R. Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation. <i>Communications in Mathematical Physics</i>. 2021;387(2):1051–1109. doi:<a href=\"https://doi.org/10.1007/s00220-021-04188-7\">10.1007/s00220-021-04188-7</a>","bibtex":"@article{Burban_Abedin_2021, title={Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation}, volume={387}, DOI={<a href=\"https://doi.org/10.1007/s00220-021-04188-7\">10.1007/s00220-021-04188-7</a>}, number={2}, journal={Communications in Mathematical Physics}, author={Burban, Igor and Abedin, R.}, year={2021}, pages={1051–1109} }","ieee":"I. Burban and R. Abedin, “Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation,” <i>Communications in Mathematical Physics</i>, vol. 387, no. 2, pp. 1051–1109, 2021, doi: <a href=\"https://doi.org/10.1007/s00220-021-04188-7\">10.1007/s00220-021-04188-7</a>."},"volume":387,"type":"journal_article","department":[{"_id":"602"}],"_id":"44329","status":"public","date_created":"2023-05-02T18:36:54Z","doi":"10.1007/s00220-021-04188-7","publication_status":"published","year":"2021","author":[{"last_name":"Burban","full_name":"Burban, Igor","id":"72064","first_name":"Igor"},{"full_name":"Abedin, R.","last_name":"Abedin","first_name":"R."}],"user_id":"49063"}