# A geometric realization of the quantum group of the circle

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Francesco Sala

created by daniele on 11 May 2018

16 may 2018
-- 15:00

Ala Contini, SNS, Pisa

**Abstract.**

Hall algebras associated with abelian categories of homological dimension one provide a geometric way to realize Hopf algebras. For example, if we consider the category of representations of a quiver over a finite field, the corresponding algebra is closely related to the quantum enveloping algebra of the Lie algebra of the quiver. In the present talk, by using the theory of Hall algebras of (stacky) curves, in particular of (the infinite) root stacks over curves, I will introduce a Lie algebra associated with the circle and its quantum enveloping algebra.