CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Professor Bodo Pareigis, Universitaet Munchen 

Time:          Wednesday, September 24, at 4:30pm 

Place:         Earth Sciences Bldg. Room 143, Univ. at Albany 

Title:         Quantum Groups - the Functorial Side     
 

(Please join us for dinner with Bodo and Karin Pareigis afterward)


Abstract:

Quantum groups or Hopf algebras can be introduced in various ways. We
want to view them as automorphism groups of noncommutative spaces or
quantum spaces.

So we first will introduce the concept of noncommutative spaces (with
noncommutative algebras as function algebras) and their
``products''. This turns out to be a categorical concept similar to the
concepts used in affine algebraic geometry. A quantum group will be an
automorphism group of a quantum space. It will then become clear to
which extent quantum groups can be viewed as groups and to which
extent the general concept of a group does not apply.

The linear representations of an ordinary group form a symmetric
tensor category. Because of their noncommutativity, quantum groups do
not have this symmetry on the tensor product of representations. In
many cases, however, it can be replaced by a braiding, for example in
the category of Yetter-Drinfeld modules or of modules over a
quasitriangular Hopf algebra.

Time permitting I will show a categorical riddle that appears in a
generalization of the definition of Yetter-Drinfeld modules, called
entwined modules: an example of a universal-couniversal problem, that
is defined by a simultaneous unit and counit.



Refreshments at 4:15 pm in ES 152.