# A Batalin-Vilkovisky structure on the complete cohomology ring of a Frobenius algebra

## TL;DR

This paper investigates the conditions under which a Batalin-Vilkovisky differential can be defined on the complete cohomology ring of a Frobenius algebra, providing a construction for cases with diagonalizable Nakayama automorphisms.

## Contribution

It introduces a method to construct a Batalin-Vilkovisky differential on the complete cohomology ring for Frobenius algebras with diagonalizable Nakayama automorphisms.

## Key findings

- Batalin-Vilkovisky differential exists for certain Frobenius algebras.
- Construction provided for algebras with diagonalizable Nakayama automorphisms.
- Advances understanding of algebraic structures in cohomology rings.

## Abstract

We study the existence of a Batalin-Vilkovisky differential on the complete cohomology ring of a Frobenius algebra.We construct a Batalin-Vilkovisky differential on the complete cohomology ring in the case of Frobenius algebras with diagonalizable Nakayama automorphisms.

---
Source: https://tomesphere.com/paper/1905.04887