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

Tomohiro Itagaki; Katsunori Sanada; Satoshi Usui

doi:10.1016/j.jalgebra.2021.04.016

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

Tomohiro Itagaki
, Katsunori Sanada
, Satoshi Usui

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	226-277
Number of pages	52
Journal	Journal of Algebra
Volume	581
DOIs	https://doi.org/10.1016/j.jalgebra.2021.04.016
Publication status	Published - 1 Sept 2021

Keywords

Batalin-Vilkovisky algebra
Complete cohomology
Frobenius algebra
Gerstenhaber algebra
Hochschild (co)homology
Tate-Hochschild cohomology

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10.1016/j.jalgebra.2021.04.016

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title = "A Batalin-Vilkovisky structure on the complete cohomology ring of a Frobenius algebra",

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.",

keywords = "Batalin-Vilkovisky algebra, Complete cohomology, Frobenius algebra, Gerstenhaber algebra, Hochschild (co)homology, Tate-Hochschild cohomology",

author = "Tomohiro Itagaki and Katsunori Sanada and Satoshi Usui",

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AU - Itagaki, Tomohiro

AU - Sanada, Katsunori

AU - Usui, Satoshi

PY - 2021/9/1

Y1 - 2021/9/1

N2 - 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.

AB - 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.

KW - Batalin-Vilkovisky algebra

KW - Complete cohomology

KW - Frobenius algebra

KW - Gerstenhaber algebra

KW - Hochschild (co)homology

KW - Tate-Hochschild cohomology

UR - https://www.scopus.com/pages/publications/85105352746

U2 - 10.1016/j.jalgebra.2021.04.016

DO - 10.1016/j.jalgebra.2021.04.016

M3 - Article

AN - SCOPUS:85105352746

SN - 0021-8693

VL - 581

SP - 226

EP - 277

JO - Journal of Algebra

JF - Journal of Algebra

ER -

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

Abstract

Keywords

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