{"citation":{"apa":"Janssens, B., & Niestijl, M. (2025). Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms. Communications in Mathematical Physics, 406(2), Article 45. https://doi.org/10.1007/s00220-024-05226-w","bibtex":"@article{Janssens_Niestijl_2025, title={Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms}, volume={406}, DOI={10.1007/s00220-024-05226-w}, number={245}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Janssens, Bas and Niestijl, Milan}, year={2025} }","short":"B. Janssens, M. Niestijl, Communications in Mathematical Physics 406 (2025).","mla":"Janssens, Bas, and Milan Niestijl. “Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms.” Communications in Mathematical Physics, vol. 406, no. 2, 45, Springer Science and Business Media LLC, 2025, doi:10.1007/s00220-024-05226-w.","ama":"Janssens B, Niestijl M. Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms. Communications in Mathematical Physics. 2025;406(2). doi:10.1007/s00220-024-05226-w","chicago":"Janssens, Bas, and Milan Niestijl. “Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms.” Communications in Mathematical Physics 406, no. 2 (2025). https://doi.org/10.1007/s00220-024-05226-w.","ieee":"B. Janssens and M. Niestijl, “Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms,” Communications in Mathematical Physics, vol. 406, no. 2, Art. no. 45, 2025, doi: 10.1007/s00220-024-05226-w."},"intvolume":" 406","year":"2025","issue":"2","publication_status":"published","publication_identifier":{"issn":["0010-3616","1432-0916"]},"doi":"10.1007/s00220-024-05226-w","title":"Generalized Positive Energy Representations of the Group of Compactly Supported Diffeomorphisms","date_created":"2026-02-20T09:33:11Z","author":[{"first_name":"Bas","last_name":"Janssens","full_name":"Janssens, Bas"},{"last_name":"Niestijl","full_name":"Niestijl, Milan","first_name":"Milan"}],"volume":406,"date_updated":"2026-02-20T09:41:41Z","publisher":"Springer Science and Business Media LLC","status":"public","abstract":[{"lang":"eng","text":"Abstract\r\n Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations \r\n \r\n $$\\overline{\\rho }$$\r\n \r\n \r\n ρ\r\n ¯\r\n \r\n \r\n \r\n of the Lie group \r\n \r\n $${{\\,\\textrm{Diff}\\,}}_c(M)$$\r\n \r\n \r\n \r\n \r\n \r\n Diff\r\n \r\n \r\n c\r\n \r\n \r\n (\r\n M\r\n )\r\n \r\n \r\n \r\n \r\n of compactly supported diffeomorphisms of a smooth manifold M that satisfy a so-called generalized positive energy condition. In particular, this captures representations that are in a suitable sense compatible with a KMS state on the von Neumann algebra generated by \r\n \r\n $$\\overline{\\rho }$$\r\n \r\n \r\n ρ\r\n ¯\r\n \r\n \r\n \r\n . We show that if M is connected and \r\n \r\n $$\\dim (M) > 1$$\r\n \r\n \r\n dim\r\n (\r\n M\r\n )\r\n >\r\n 1\r\n \r\n \r\n \r\n , then any such representation is necessarily trivial on the identity component \r\n \r\n $${{\\,\\textrm{Diff}\\,}}_c(M)_0$$\r\n \r\n \r\n \r\n \r\n \r\n Diff\r\n \r\n \r\n c\r\n \r\n \r\n \r\n (\r\n M\r\n )\r\n \r\n 0\r\n \r\n \r\n \r\n \r\n . As an intermediate step towards this result, we determine the continuous second Lie algebra cohomology \r\n \r\n $$H^2_\\textrm{ct}(\\mathcal {X}_c(M), \\mathbb {R})$$\r\n \r\n \r\n \r\n H\r\n ct\r\n 2\r\n \r\n \r\n (\r\n \r\n X\r\n c\r\n \r\n \r\n (\r\n M\r\n )\r\n \r\n ,\r\n R\r\n )\r\n \r\n \r\n \r\n \r\n of the Lie algebra of compactly supported vector fields. This is subtly different from Gelfand–Fuks cohomology in view of the compact support condition."}],"type":"journal_article","publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}],"article_number":"45","user_id":"104095","department":[{"_id":"93"}],"_id":"64289"}