Around the center
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918154546970624 |
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| author | Gorelik, Maria Hinich, Vladimir Serganova, Vera |
| author_facet | Gorelik, Maria Hinich, Vladimir Serganova, Vera |
| contents | The center of a semisimple Lie algebra can be described as the algebra of W-invariant functions on the dual of the Cartan subalgebra. The centers of many Lie superalgebras have a similar description, but the defining equivalence relation on the dual of the Cartan subalgebra is not given by a finite group action. Lagrangian equivalence relations that we introduce generalize the action of a subgroup of the orthogonal group. Using them, we present a new proof of a result by Ian Musson about the centers of Lie superalgebras. Our proof is not based on a case-by-case analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Around the center Gorelik, Maria Hinich, Vladimir Serganova, Vera Representation Theory 17B10, 17B20, 17B67 The center of a semisimple Lie algebra can be described as the algebra of W-invariant functions on the dual of the Cartan subalgebra. The centers of many Lie superalgebras have a similar description, but the defining equivalence relation on the dual of the Cartan subalgebra is not given by a finite group action. Lagrangian equivalence relations that we introduce generalize the action of a subgroup of the orthogonal group. Using them, we present a new proof of a result by Ian Musson about the centers of Lie superalgebras. Our proof is not based on a case-by-case analysis. |
| title | Around the center |
| topic | Representation Theory 17B10, 17B20, 17B67 |
| url | https://arxiv.org/abs/2510.03928 |