Hopf actions on vertex algebras

2023/10/12 by Chongying Dong, Li Ren, Dong, Chongying +3 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2310.08506

Abstract

In this article, we investigate Hopf actions on vertex algebras. Our first main result is that every finite-dimensional Hopf algebra that inner faithfully acts on a given π₂-injective vertex algebra must be a group algebra. Secondly, under suitable assumptions, we establish a Schur-Weyl type duality for semisimple Hopf actions on Hopf modules of vertex algebras.

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• Y(z)-injective vertex superalgebras and Hopf actions

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