A Batalin-Vilkovisky structure on the complete cohomology ring of a Frobenius algebra
Tomohiro Itagaki, Katsunori Sanada, Satoshi Usui
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.
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry