Many of the standard sources which discuss the Hochschild Kostant Rosenberg theorem and cyclic homology for smooth varieties such as Loday and Weibel's paper "The Hodge Filtration …

Arinkin has a theorem which says that an abelian variety can be reconstructed from its derived category of coherent D-modules. D.Orlov conjectured that this theorem is true for a …

I just took a look at the nlab entry: Nikolai Durov. It seems that Skoda never mentioned that what Durov introduced was a special case of generalized scheme theory. I did not read …

I have sitting in front of me two 2-categories. On the left, I have the 2-category GPOID, whose: objects are groupoids; 1-morphisms are (left-principal?) bibundles; 2-morphisms …

I want to consider a Z/2Z dg algebra. As an algebra, it is generated over $\mathbb{Q}$ by two elements where x is even and e is odd with the relations $xe=ex$ and $e^2=1$(this make …

Michel Van den Bergh introduced the notion of a double Poisson algebra. The definition is cooked up such that the representation varieties of such an algebra are Poisson varieties. …

This is a follow up to my question What is the precise relationship between groupoid language and noncommutative algebra language?. I will briefly review some definitions; for det …

Suppose I tried to take Hartshorne chapter II and re-do all of it with non-commutative rings rather than commutative rings. Is this possible? Which parts work in the non-commutativ …

This question is the outcome of a few naive thoughts, without reading the proof of Gelfand-Neumark theorem. Given a compact Hausdorff space $X$, the algebra of complex continuous …

For a group $G$, is there an interpretation of $\mathbb{C}[G]$ as functions over some noncommutative space? If so, what does this space "look like"? What are its properties? How …

Group von Neumann algebras and crossed products for a locally compact group G can be constructed in many different ways. For example, one can take the von Neumann algebra generated …

It might be a stupid question. How to glue perverse sheaves? I am considering the following example. Flag variety of $sl_2$, which is $P^1$. Consider category of perverse sheaves …

How much is known about the Weyl character formula for quantum groups? More specifically, has the formula been generalized to the general setting of deformed coordinate algebras $\ …

The fact that a commutative ring has a natural topological space associated with it is still a really interesting coincidence. The entire subject of Algebraic geometry is based on …

Several times I have come across these algebras and I wonder why any of these are interesting; I'm very sure they are, but I could not find an answer in the literature. For examp …