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Article: Shifted Poisson geometry and meromorphic matrix algebras over an elliptic curve
Title | Shifted Poisson geometry and meromorphic matrix algebras over an elliptic curve |
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Authors | |
Issue Date | 2019 |
Publisher | Birkhaeuser Verlag AG. The Journal's web site is located at http://link.springer.de/link/service/journals/00029/index.htm |
Citation | Selecta Mathematica, 2019, v. 25 n. 3, article no. 42 How to Cite? |
Abstract | In this paper we classify symplectic leaves of the regular part of the projectivization of the space of meromorphic endomorphisms of a stable vector bundle on an elliptic curve, using the study of shifted Poisson structures on the moduli of complexes from our previous work (Hua and Polishchuk in Adv Math 338:991–1037, 2018). This Poisson ind-scheme is closely related to the ind Poisson–Lie group associated to Belavin’s elliptic r-matrix, studied by Sklyanin, Cherednik and Reyman and Semenov-Tian-Shansky. Our result leads to a classification of symplectic leaves on the regular part of meromorphic matrix algebras over an elliptic curve, which can be viewed as the Lie algebra of the above-mentioned ind Poisson–Lie group. We also describe the decomposition of the product of leaves under the multiplication morphism and show the invariance of Poisson structures under autoequivalences of the derived category of coherent sheaves on an elliptic curve. |
Persistent Identifier | http://hdl.handle.net/10722/275729 |
ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 1.715 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Hua, Z | - |
dc.contributor.author | Polishchuk, A | - |
dc.date.accessioned | 2019-09-10T02:48:30Z | - |
dc.date.available | 2019-09-10T02:48:30Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | Selecta Mathematica, 2019, v. 25 n. 3, article no. 42 | - |
dc.identifier.issn | 1022-1824 | - |
dc.identifier.uri | http://hdl.handle.net/10722/275729 | - |
dc.description.abstract | In this paper we classify symplectic leaves of the regular part of the projectivization of the space of meromorphic endomorphisms of a stable vector bundle on an elliptic curve, using the study of shifted Poisson structures on the moduli of complexes from our previous work (Hua and Polishchuk in Adv Math 338:991–1037, 2018). This Poisson ind-scheme is closely related to the ind Poisson–Lie group associated to Belavin’s elliptic r-matrix, studied by Sklyanin, Cherednik and Reyman and Semenov-Tian-Shansky. Our result leads to a classification of symplectic leaves on the regular part of meromorphic matrix algebras over an elliptic curve, which can be viewed as the Lie algebra of the above-mentioned ind Poisson–Lie group. We also describe the decomposition of the product of leaves under the multiplication morphism and show the invariance of Poisson structures under autoequivalences of the derived category of coherent sheaves on an elliptic curve. | - |
dc.language | eng | - |
dc.publisher | Birkhaeuser Verlag AG. The Journal's web site is located at http://link.springer.de/link/service/journals/00029/index.htm | - |
dc.relation.ispartof | Selecta Mathematica | - |
dc.title | Shifted Poisson geometry and meromorphic matrix algebras over an elliptic curve | - |
dc.type | Article | - |
dc.identifier.email | Hua, Z: huazheng@hku.hk | - |
dc.identifier.authority | Hua, Z=rp01790 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00029-019-0489-4 | - |
dc.identifier.scopus | eid_2-s2.0-85067473509 | - |
dc.identifier.hkuros | 302961 | - |
dc.identifier.hkuros | 289659 | - |
dc.identifier.volume | 25 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | article no. 42 | - |
dc.identifier.epage | article no. 42 | - |
dc.identifier.isi | WOS:000472231200001 | - |
dc.publisher.place | Switzerland | - |
dc.identifier.issnl | 1022-1824 | - |