Cellular resolutions of noncommutative toric algebras from superpotentials
Alexander Quintero Velez (University of Glasgow)
Monday 22nd November, 2010 16:00-17:00 204
A dimer model is a bipartite graph embedded in a real 2-torus. Every such graph determines naturally a noncommutative algebra A whose centre is a semigroup algebra R. Under mild assumptions, it has been shown that the dimer model encodes the minimal projective resolution of A as an (A,A)-bimodule and, moreover, that A is a CY3-algebra (it is a "noncommutative crepant resolution" of R). In this talk I will describe how to construct the resolution much more simply from a toric cell complex. This "noncommutative cellular resolution" provides an analogue of the cellular resolutions in commutative algebra constructed by Bayer-Sturmfels, and it makes possible a generalization of the dimer model construction to arbitrary dimension. This is joint work with Alastair Craw.