Oriented Algebras and the Hochschild Cohomology Group

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) over tilde (G)*(A, X). In this paper, we form a new bicomplex (sic)(G)* (A, X) by deleting the first column and the first row and reindexing. We show that (1)((sic)G) (A, X) classifies the singular extensions of oriented algebras.