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June 2023 Batalin-Vilkovisky algebra structures on the Hochschild cohomology of self-injective Nakayama algebras
Tomohiro Itagaki
Author Affiliations +
SUT J. Math. 59(1): 33-59 (June 2023). DOI: 10.55937/sut/1686053151

Abstract

In this paper, we determine the Batalin-Vilkovisky algebra structure on the Hochschild cohomology of self-injective Nakayama algebras with the diagonalizable Nakayama automorphism over an algebraically closed field K. Moreover, in the case that the characteristic of K divides the order of the Nakayama automorphism, we compute the Batalin-Vilkovisky algebra structure on cohomology of Hochschild complex related to the Nakayama automorphism.

Funding Statement

This work was supported by JSPS KAKENHI Grant Number 17K14175.

Acknowledgments

The author thanks Professor Guodong Zhou and Professor Yury Volkov for important comments on a Batalin-Vilkovisky algebra structure on Hochschild cohomology. Moreover, he enjoyed very much being a member of the representation theory group in Stuttgart and he thanks the colleagues for hospitality. He also thanks the referee for many variable comments.

Citation

Download Citation

Tomohiro Itagaki. "Batalin-Vilkovisky algebra structures on the Hochschild cohomology of self-injective Nakayama algebras." SUT J. Math. 59 (1) 33 - 59, June 2023. https://doi.org/10.55937/sut/1686053151

Information

Received: 3 October 2022; Published: June 2023
First available in Project Euclid: 19 July 2023

zbMATH: 07733548
Digital Object Identifier: 10.55937/sut/1686053151

Subjects:
Primary: 16E40

Keywords: Batalin-Vilkovisky structure , Frobenius algebra , Gerstenhaber algebra , Hochschild cohomology , self-injective Nakayama algebra

Rights: Copyright © 2023 Tokyo University of Science

Vol.59 • No. 1 • June 2023
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