Frobenius W-algebras and traces of Frobenius Heisenberg categories

TL;DR

This paper constructs a new W-algebra from symmetric graded Frobenius superalgebras and establishes a conjectured isomorphism with the trace of Frobenius Heisenberg categories, linking algebraic structures.

Contribution

It introduces a novel W-algebra associated to symmetric graded Frobenius superalgebras and proposes a conjecture relating it to the trace of Frobenius Heisenberg categories.

Findings

Defined a W-algebra from symmetric graded Frobenius superalgebras

Established a linear isomorphism with the trace of Frobenius Heisenberg category

Conjectured an isomorphism of graded superalgebras

Abstract

To each symmetric graded Frobenius superalgebra we associate a W-algebra. We then define a linear isomorphism between the trace of the Frobenius Heisenberg category and a central reduction of this W-algebra. We conjecture that this is an isomorphism of graded superalgebras.