On Abelianity Lines in Elliptic -Algebras
We present a systematic derivation of the abelianity conditions for the q-deformed -algebras constructed from the elliptic quantum algebra Aq,ₚ(ˆ()c). We identify two sets of conditions on a given critical surface yielding abelianity lines in the moduli space (, , ). Each line is identified as an in...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211026 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On Abelianity Lines in Elliptic -Algebras. Jean Avan, Luc Frappat and Eric Ragoucy. SIGMA 16 (2020), 094, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862553529652084736 |
|---|---|
| author | Avan, Jean Frappat, Luc Ragoucy, Eric |
| author_facet | Avan, Jean Frappat, Luc Ragoucy, Eric |
| citation_txt | On Abelianity Lines in Elliptic -Algebras. Jean Avan, Luc Frappat and Eric Ragoucy. SIGMA 16 (2020), 094, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present a systematic derivation of the abelianity conditions for the q-deformed -algebras constructed from the elliptic quantum algebra Aq,ₚ(ˆ()c). We identify two sets of conditions on a given critical surface yielding abelianity lines in the moduli space (, , ). Each line is identified as an intersection of a countable number of critical surfaces obeying diophantine consistency conditions. The corresponding Poisson bracket structures are then computed, for which some universal features are described.
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| first_indexed | 2026-03-13T05:29:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211026 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T05:29:24Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Avan, Jean Frappat, Luc Ragoucy, Eric 2025-12-22T09:32:08Z 2020 On Abelianity Lines in Elliptic -Algebras. Jean Avan, Luc Frappat and Eric Ragoucy. SIGMA 16 (2020), 094, 18 pages 1815-0659 2020 Mathematics Subject Classification: 17B37; 17B68 arXiv:2005.03579 https://nasplib.isofts.kiev.ua/handle/123456789/211026 https://doi.org/10.3842/SIGMA.2020.094 We present a systematic derivation of the abelianity conditions for the q-deformed -algebras constructed from the elliptic quantum algebra Aq,ₚ(ˆ()c). We identify two sets of conditions on a given critical surface yielding abelianity lines in the moduli space (, , ). Each line is identified as an intersection of a countable number of critical surfaces obeying diophantine consistency conditions. The corresponding Poisson bracket structures are then computed, for which some universal features are described. Part of this work was done during the visit of J.A. to LAPTh, with financial support from the USMB grant AAP ASI-32. We also wish to thank the referees for their fruitful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Abelianity Lines in Elliptic -Algebras Article published earlier |
| spellingShingle | On Abelianity Lines in Elliptic -Algebras Avan, Jean Frappat, Luc Ragoucy, Eric |
| title | On Abelianity Lines in Elliptic -Algebras |
| title_full | On Abelianity Lines in Elliptic -Algebras |
| title_fullStr | On Abelianity Lines in Elliptic -Algebras |
| title_full_unstemmed | On Abelianity Lines in Elliptic -Algebras |
| title_short | On Abelianity Lines in Elliptic -Algebras |
| title_sort | on abelianity lines in elliptic -algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211026 |
| work_keys_str_mv | AT avanjean onabelianitylinesinellipticalgebras AT frappatluc onabelianitylinesinellipticalgebras AT ragoucyeric onabelianitylinesinellipticalgebras |