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Green-type theorems for representations of Hall algebras

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If you have a question about this talk, please contact Lewis Topley.

Associated to a suitably finite abelian category is its Hall algebra, an associative algebra which encodes the first order extension structure of the category. A choice of duality structure on the category defines a module over the Hall algebra which encodes the first order orthogonal/symplectic extension structure. The goal of this talk is to introduce this class of modules and explain their relevance to the theory of quantum groups and Donaldson-Thomas theory. A key gap in our understanding is the lack of result describing the compatibility of the module structure with a natural comodule structure; the analogous result for Hall algebras is called Green’s theorem. I will describe such a Green-type theorem in the simpler setting of categories which are linear over the field with one element, and discuss its potential implications for Donaldson-Thomas theory.

This talk is part of the Algebra seminar series.

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