A new family of algebras whose representation schemes are smooth

Abstract

We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field of characteristic zero. In particular, our result implies that the points M of the above scheme, satisfying $Ext_A ^2(M,M)=0$, are regular. This generalizes well-known results on finite-dimensional algebras to finitely generated algebras.