Tagged Questions

3
votes
0answers
177 views

Hochschild and cyclic homology of smooth varieties

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 …
5
votes
1answer
247 views

Reconstruction from category of D-modules on variety

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 …
6
votes
2answers
298 views

Did Durov’s work give an example of noncommutative schemes?

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 …
11
votes
3answers
320 views

What is the precise relationship between groupoid language and noncommutative algebra language?

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 …
4
votes
0answers
258 views

A smooth twisted tensor product of dg algebras?

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 …
0
votes
0answers
299 views

What is a “double star-product”

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. …
4
votes
2answers
225 views

Is a groupoid determined by its Hopfish algebra?

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 …
34
votes
11answers
2k views

Non-commutative algebraic geometry

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 …
7
votes
3answers
429 views

Relevance of the complex structure of a function algebra for capturing the topology on a space.

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 …
14
votes
2answers
452 views

Geometric interpretation of group rings?

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 …
3
votes
1answer
249 views

Universal characterization and explicit description of elements of the group von Neumann algebra and the crossed product

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 …
5
votes
4answers
562 views

Gluing perverse sheaves?

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 …
5
votes
1answer
210 views

Weyl Character Formula for Quantum Groups

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 $\ …
18
votes
6answers
1k views

“Algebraic” topologies like the Zariski topology?

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 …
12
votes
3answers
391 views

What are the motivations for studying Cherednik (symplectic reflection, graded Hecke) algebras?

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 …

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