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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211078 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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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| ISSN: | 1815-0659 |