Quantum differentials on U_q(g) and q-fuzzy spheres

Shahn Majid (Queen Mary)

Wednesday 4th November, 2009 16:00-17:00 Mathematics Building, Room 204

Abstract

Just as the enveloping algebra U(g) of a Lie algebra g can be viewed as a quantisation of g*, we consider quantum groups U_q(g) as a quantisation or `coordinate algebra'. We pose the question of their natural noncommutative differential calculus in the sense of a differential graded algebra, and find a canonical answer using braided category methods. We obtain explicit results for the case of the algebra U_q(su_2) and the q-hyperboloid of which it is a localisation, and show that the noncommutative differential geometry of the latter is obtained systematically from the noncommutative differential geometry of C_q(SU_2) by a (twist)-equivalence of comodule categories. The non-standard Podles spheres naturally turn out to be cross-sections of this same q-hyperboloid and we provide a braided category approach their construction. If time, recent progress on some other noncommutative differential geometries of mathematical interest will be covered.

Add to your calendar

Download event information as iCalendar file (only this event)