Oriented algebras and the Hochschild cohomology group (Q1634695)

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.