Abstract
Koam and Pirashivili developed the equivariant version of Hochschild cohomology by mixing the standard chain complexes computing group with associative algebra cohomologies to obtain the bicomplex C ˜ G * ( A , X ). In this paper, we form a new bicomplex F ˘ G * ( A , X ) by deleting the first column and the first row and reindexing. We show that H ˘ G 1 ( A , X ) classifies the singular extensions of oriented algebras.
Highlights
One of the main applications of homological algebra is the classical cohomology of associative algebras invented by Hochschild [1] in 1945
It is a particular case of general machinery developed by Cartan and Eilenberg
An oriented algebra is an associative algebra A equipped with a G-module structure ( g, a) 7→ g a, satisfying the condition
Summary
One of the main applications of homological algebra is the classical cohomology of associative algebras invented by Hochschild [1] in 1945. It is a particular case of general machinery developed by Cartan and Eilenberg. The low dimensional groups (n2) have well known interpretations of classical algebraic structures such as derivations and extensions [2,3,4]. An oriented algebra is an associative algebra A equipped with a G-module structure ( g, a) 7→ g a, satisfying the condition The aim of this work is to prove that H1G ( A, X ) classifies the singular extensions of oriented algebras. We obtain a new bicomplex by deleting the first column and the first row and reindexing
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