A generalised Kac-Peterson cocycle 11:10 Thu 17 Apr, 2014 :: Ingkarni Wardli B20 :: Pedram Hekmati :: University of Adelaide
The Kac-Peterson cocycle appears in the study of highest weight modules of infinite dimensional Lie algebras and determines a central extension. The vanishing of its cohomology class is tied to the existence of a cubic Dirac operator whose square is a quadratic Casimir element. I will introduce a closely related Lie algebra cocycle that comes about when constructing spin representations and gives rise to a Banach Lie group with a highly nontrivial topology. I will also explain how to make sense of the cubic Dirac operator in this setting and discuss its relation to twisted K-theory. This is joint work with Jouko Mickelsson.