Abstract:
Hochschild (co)homology spaces are homological invariants of associative algebras that are useful to describe several properties of the concerned algebra. In this talk we will focus on geometric regularity. If the algebra is commutative and finitely generated, then Hochschild homology can be used to decide whether the associated algebraic variety is regular or not. In the non-commutative case, the meaning of all this is not so clear. In this talk I will first describe Hochschild (co)homology and the results that are known in the commutative setting, and I will comment afterwards on the non-commutative case.