Twisted associative algebras associated to vertex algebras
Shun Xu

TL;DR
This paper constructs a sequence of associative algebras linked to vertex algebras with automorphisms, demonstrating that certain properties of vertex operator algebras are independent of their conformal structure.
Contribution
It introduces a new family of associative algebras associated to vertex algebras with automorphisms, independent of conformal structure, and explores their implications.
Findings
Constructed associative algebras $ ilde{A}_{g,n}(V)$ for vertex algebras.
Showed $g$-rationality and $g$-regularity are conformal vector independent.
Established twisted fusion rules are independent of conformal vector choice.
Abstract
Let be a vertex algebra and an automorphism of of order . We construct a sequence of associative algebras for any , which are not depend on the conformal structure of . We show that for a vertex operator algebra, -rationality, -regularity, and twisted fusion rules are independent of the choice of the conformal vector.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras
