Extension Quiver for Lie Superalgebra (3)
We describe all blocks of the category of finite-dimensional (3)-supermodules by providing their extension quivers. We also obtain two general results about the representation of (): we show that the Ext quiver of the standard block of () is obtained from the principal block of ( − 1) by identifying...
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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/123456789/211078 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Extension Quiver for Lie Superalgebra (3). Nikolay Grantcharov and Vera Serganova. SIGMA 16 (2020), 141, 32 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862628088542658560 |
|---|---|
| author | Grantcharov, Nikolay Serganova, Vera |
| author_facet | Grantcharov, Nikolay Serganova, Vera |
| citation_txt | Extension Quiver for Lie Superalgebra (3). Nikolay Grantcharov and Vera Serganova. SIGMA 16 (2020), 141, 32 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We describe all blocks of the category of finite-dimensional (3)-supermodules by providing their extension quivers. We also obtain two general results about the representation of (): we show that the Ext quiver of the standard block of () is obtained from the principal block of ( − 1) by identifying certain vertices of the quiver and proving a ''virtual'' BGG-reciprocity for (). The latter result is used to compute the radical filtrations of (3) projective covers.
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| first_indexed | 2026-03-14T16:30:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211078 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T16:30:25Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Grantcharov, Nikolay Serganova, Vera 2025-12-23T13:11:15Z 2020 Extension Quiver for Lie Superalgebra (3). Nikolay Grantcharov and Vera Serganova. SIGMA 16 (2020), 141, 32 pages 1815-0659 2020 Mathematics Subject Classification: 17B55; 17B10 arXiv:2008.10649 https://nasplib.isofts.kiev.ua/handle/123456789/211078 https://doi.org/10.3842/SIGMA.2020.141 We describe all blocks of the category of finite-dimensional (3)-supermodules by providing their extension quivers. We also obtain two general results about the representation of (): we show that the Ext quiver of the standard block of () is obtained from the principal block of ( − 1) by identifying certain vertices of the quiver and proving a ''virtual'' BGG-reciprocity for (). The latter result is used to compute the radical filtrations of (3) projective covers. The authors would like to thank Dimitar Grantcharov for numerous helpful discussions. N.G. was supported by NSF grant DGE 1746045, and V.S. was supported by NSF grant 1701532. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Extension Quiver for Lie Superalgebra (3) Article published earlier |
| spellingShingle | Extension Quiver for Lie Superalgebra (3) Grantcharov, Nikolay Serganova, Vera |
| title | Extension Quiver for Lie Superalgebra (3) |
| title_full | Extension Quiver for Lie Superalgebra (3) |
| title_fullStr | Extension Quiver for Lie Superalgebra (3) |
| title_full_unstemmed | Extension Quiver for Lie Superalgebra (3) |
| title_short | Extension Quiver for Lie Superalgebra (3) |
| title_sort | extension quiver for lie superalgebra (3) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211078 |
| work_keys_str_mv | AT grantcharovnikolay extensionquiverforliesuperalgebra3 AT serganovavera extensionquiverforliesuperalgebra3 |