I have often heard the slogan that "a matrix algebra has no deformations," and I am trying to understand precisely what that means. While I would be happy with more general statements about ...
I am wondering if there is a nice presentation of the Hochschild cohomology of $A_n$ the Weyl algebra. It is known that $H^m(A_n,A_n)=0$ for $m>0$, and thus it is rigid. A proof can be found in ...
Background: in deformation quantization one wants to construct formal associative deformations (the star products $\star$) of the algebra of smooth complex-valued functions on a Poisson manifold $M$ ...
From the discussion here, it seems that general Hochschild cohomology classes correspond to deformations where the deformation parameter can have nonzero degree. So I have some naive and maybe stupid ...
When we are dealing with ordinary things or dg things (where thing = algebra or category), I think I understand how HH^2 corresponds to 1st order deformations and HH^3 corresponds to obstructions. ...