Tensor Hochschild homology and cohomology

Claude Cibils
 
 
 
 
We consider the non commutative setting given by a ring A, an A-bimodule M and T the corresponding tensor algebra. We prove that the Hochschild cohomology of quotients T/I by positive ideals coincides with the homology of A whenever the quiver of M has no oriented cycles. 

If the quiver is an arrow (i.e. T is a triangular two by two matrix algebra) the Hochschild cohomology belongs to a long exact sequence. For other quivers, a spectral sequence converging to the Hochschild cohomology will be described in a forthcoming paper. 

 
 
 .dvi 
 

Claude Cibils
 

Dép. de mathématiques, Université de Montpellier 2                                   Retour