Oriented algebras and the Hochschild cohomology group
type: Item
instance of: scholarly article
title: Oriented algebras and the Hochschild cohomology group
zbMATH Open document ID: 1409.16002
author: Ali N. A. Koam
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: The author and \textit{T. Pirashvili} [Commun. Algebra 46, No. 7, 2947--2963 (2018; Zbl 1427.16006)] developed the equivariant version of Hochschild cohomology by mixing the standard chain complexes computing group with associative algebra cohomologies to obtain the bicomplex \(\widetilde{C}_G^\ast (A, X)\). In this paper, we form a new bicomplex \(\breve{F}_G^\ast (A, X)\) by deleting the first column and the first row and reindexing. We show that \(\breve{\mathcal H}_G^1(A, X)\) classifies the singular extensions of oriented algebras.
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 18G60
zbMATH DE Number: 6994840
zbMATH Keywords: group cohomology
zbMATH Keywords: Hochschild cohomology
zbMATH Keywords: oriented algebras
MaRDI profile type: Publication
full work available at URL: math6110237
OpenAlex ID: W2899289968
cites work: On the cohomology groups of an associative algebra
cites work: Comparison of MacLane, Shukla and Hochschild cohomologies
cites work: Q4367927
cites work: Cohomology of oriented algebras
DOI: 10.3390/MATH6110237
description: scientific article; zbMATH DE number 6994840