Representation theory seminar and center of excellence QuantiXLie

 

Tuesday, September 15 at 17:15, room 109

 

Alessandro Carotenuto: Differential calculi for quantum groups

 

In this first talk we will introduce the basic notion of a differential calculus in Noncommutative Geometry .and develop the theory for quantum groups. I will explicitly discuss the construction of covariant differential calculi for Drinfeld—Jimbo quantum coordinate algebras, in the light of the fundamental theorem of Hopf algebras.

Time allowing I will go into details in the description of some differential calculi of historical significance for the development of the theory.

In the forthcoming talks, these tools will be fundamental to describe differential calculi over quantum homogeneous spaces, which constitute a sub-class of left coideal subalgebras, and to develop the corresponding Noncommutative Geometric representation theory.