I recently heard a talk about these topics and found them very interesting. The talk was centered on the formal structure and didn't really focus on examples. So my question is: w …

Suppose $X$ is a smooth algebraic variety over a field of characteristic $0$. What are the most general conditions under which Hochschild homology and cohomology of $X$ agree? The …

In Mariusz Wodzicki's paper "Cyclic homology of differential operators," the following result is mentioned: for $D_M$ the algebra of differential operators on a smooth manifold $M$ …

Let A with d be a differential graded associative algebra (DG algebra). What is the definition of Hochschild complex C*(A,A)? There should be a Hoshschild differential and a cup p …

I have often heard the slogan that "a matrix algebra algebra has no deformations," and I am trying to understand precisely what that means. While I would be happy with more genera …

Hi, I wonder if there is a name for: 1) Algebras which are Morita equivalent to their centers, or 2) dg-algebras which are derived Morita equivalent to their Hochshild cohomolog …

Hello, I would like to experiment with André-Quillen (co)homology. Especially for singular rings. A key problem is that the construction of a simplicial resolution of a ring seems …

There is currently no treatise treating Hochschild (co)homology systematically. There is a chapter in Weibel's book, there's parts of Loday's and a few others... What should be …

Let $C$ be an arbitrary algebra (more generally, a linear 1-category). The following structures are well-known: A degree-0 product on the Hochschild cohomology $HH^*(C)$ $$ HH^* …

This is shamelessly close to my other question: http://mathoverflow.net/questions/70151/a-question-on-koszul-duality-and-b-infty-structures-on-hh. Maybe this one will get a better …

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 ca …

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 Po …

Let $X$ be a quasi-projective variety over a field $k$. Let $D_{qcoh}$ be a dg enhancement of the unbounded derived category of quasi-coherent sheaves over $X$, and $D_{perf}$ its …

The following theorem is known from a paper "Duality in Gerstenhaber Algebras" by Felix, Menichi, Thomas. Given a simply connected space X of finite type. There is an equivalence …

Let $k$ be a commutative ring (with unity). Let $R$ be a $k$-algebra (with unity, but not of necessity commutative). Let $M$ be an $\left(R,R\right)$-bimodule where $k$ acts in th …