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 $Ex{t}_A^2(M,M)=0$, are regular. This generalizes well-known results on finite-dimensional algebras to finitely generated algebras.

15 pages. Accepted for publication in Annales De L'Institut Fourier

References in corpus (5)

• Calabi-Yau algebras
• Lectures on Noncommutative Geometry
• Cohomology of non-commutative Hilbert schemes
• A converse to the Second Whitehead Lemma
• Noncommutative Tangent Cones and Calabi Yau Algebras