Deformation of modules over noncommutaitve rings - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T18:51:59Z http://mathoverflow.net/feeds/question/106798 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106798/deformation-of-modules-over-noncommutaitve-rings Deformation of modules over noncommutaitve rings Muon 2012-09-10T09:33:35Z 2012-09-11T22:58:21Z <p>Let $M$ be a finitely generated module over a commutative ring $R$. The first order deformation of module $M$ is parametrized by $Ext^{1}(M,M)$ and the obstruction is parametrized by $Ext^{2}(M,M)$. Is there a similar story for noncommutative $R$? I don't expect this to be true for any noncommutative rings but wonder if this is still true for some $good$ ones. I would appreciate any reference suggestion, comments, and ideas. </p> <p><strong>Edit</strong> I would like naively to compute the tangent space of the moduli space $X$ of module with some data if it exists. At $M\in X$, the tangent space can be understood as the set of extensions of the $R$-module $M$ to some $R\otimes_{k} k[\epsilon]/(\epsilon^2)$-module. The obstruction is defined in the same manner. </p>