Mathematical Sciences Research Institute

Home » Noncommutative Clusters (NAGRT)


Noncommutative Clusters (NAGRT) May 22, 2013 (03:30 PM PDT - 04:30 PM PDT)
Parent Program:
Location: MSRI: Simons Auditorium
Speaker(s) Arkady Berenstein (University of Oregon)
Description No Description
No Video Uploaded

Cluster algebras were introduced by Fomin and Zelevinsky in 2001 and have become an important tool in representation theory, higher category theory, and algebraic/Poisson geometry.

The goal of my talk (based on a joint paper with V. Retakh) is to introduce totally noncommutative clusters and their mutations, which can be viewed as generalizations of both ``classical" and quantum cluster structures.

Each noncommutative cluster X is built on a torsion-free group G and a certain collection of its automorphisms. We assign to X a noncommutative algebra A(X) related to the group algebra of G, which is an analogue of the cluster algebra, and expect a Noncommutative Laurent Phenomenon to hold in the most of algebras A(X).

Our main examples of "cluster groups" G include principal noncommutative tori which we define for any initial exchange matrix B and noncommutative triangulated groups which we define for all oriented surfaces.

No Notes/Supplements Uploaded No Video Files Uploaded