Twisted Zhu algebras
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913500429811712 |
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| author | Genra, Naoki |
| author_facet | Genra, Naoki |
| contents | Let $V$ be a freely generated pregraded vertex superalgebra, $H$ a Hamiltonian operator of $V$, and $g$ a diagonalizable automorphism of V commuting with $H$ with modulus $1$ eigenvalues. We prove that the $(g, H)$-twisted Zhu algebra of $V$ has a PBW basis, is isomorphic to the universal enveloping algebra of some non-linear Lie superalgebra, and satisfies the commutativity of BRST cohomology functors, which generalizes results of De Sole and Kac. As applications, we compute the twisted Zhu algebras of affine vertex superalgebras and affine $W$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted Zhu algebras Genra, Naoki Representation Theory Quantum Algebra Let $V$ be a freely generated pregraded vertex superalgebra, $H$ a Hamiltonian operator of $V$, and $g$ a diagonalizable automorphism of V commuting with $H$ with modulus $1$ eigenvalues. We prove that the $(g, H)$-twisted Zhu algebra of $V$ has a PBW basis, is isomorphic to the universal enveloping algebra of some non-linear Lie superalgebra, and satisfies the commutativity of BRST cohomology functors, which generalizes results of De Sole and Kac. As applications, we compute the twisted Zhu algebras of affine vertex superalgebras and affine $W$-algebras. |
| title | Twisted Zhu algebras |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2409.09656 |