Evento
Descrizione:
A Hopf algebra H over a field k is an ordinary associative and unital k-algebra enriched with three additional structures: a coassociative comultiplication D : H -> H\otimes H, a counit e : H -> k and an inversion (or antipode) S : H -> H. One of their striking features is that they naturally arise in a wide number of settings: in Lie theory as universal enveloping algebras of Lie algebras, in algebraic geometry as algebras of regular functions on affine algebraic groups, in differential geometry as algebras of representative functions on compact Lie groups, in group theory as group rings of abstract groups. The aim of this seminar is to give an insight into the interplay between Hopf algebra theory and geometry. We plan to recall briefly what a Hopf algebra is, how some of the aforementioned connections are built and eventually, time permitting, to say a few words about Hopf algebroids and their connection with groupoids and Lie algebroids.