扭曲朱代数

arXiv - MATH - Representation Theory Pub Date : 2024-09-15 DOI:arxiv-2409.09656

Naoki Genra

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引用次数: 0

摘要

设 $V$ 是一个自由生成的预分级顶点超代数，$H$ 是 $V$ 的哈密顿算子，$g$ 是 V 的一个可对角的自变量，与具有模 1$ 特征值的 $H$ 交乘。我们证明$V$的$(g,H)$扭曲朱代数有一个PBW基，与某个非线性李超代数的普遍展开代数同构，并满足BRST同调函数的交换性，这概括了德索兰-卡克的结果。作为应用，我们计算了仿射顶点上代数和仿射 $W$-gebras 的扭曲朱代数。

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Twisted Zhu algebras

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.

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arXiv - MATH - Representation Theory

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