Mathematisches Kolloquium

Zusammenfassung: Around 1985 Drinfeld and Jimbo discovered one-parameter deformations of the universal enveloping algebras od the semisimple complex Lie algebras. These new algebras are Hopf algebras and typical examples of quantum groups in the sense of Drinfeld's lecture at the ICM in Berkeley 1986. A few years later Lusztig introduced finete-dimensional versions, the so-called small quantum groups. All these quantum groups are pointed as Hopf algebras, that is, their simple comodules are 1-dimensional. In this talk I will explain quantum groups and Hopf algebras. Then I will discuss recent results of a joint project with N. Anduskiewitsch on the classification of pointed Hopf algebras. We classify finite-dimensional pointed Hopf algebras over the complex numbers with abelian group of group-like elements (and such that all prime divisors of the order of this group are >7). It turns out that all these Hopf algebras are deformations of natural generalizations of the small quantum groups. Hence our result can also be read as an axiomatic description of generalized small quantum groups.

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

Treffpunkt zum Abendessen um 19.00 Uhr wird noch bekannt gegeben.