University of Sydney Algebra Seminar

Yang Zhang (University of Sydney)

Friday 18 October, 12-1pm, Place: Carslaw 375

Noncrossing algebras associated to finite Coxeter groups

For any finite Coxeter group there is a noncrossing partition lattice (NCP) comprising elements between the identity and a fixed Coxeter element. In analogy with the Orlik-Solomon algebras, I will define the noncrossing algebra associated to any NCP in two different ways. The first definition is given in terms of generators and relations with some baby examples. On the other hand, I will show that braid group actions on the chains of NCP can produce a finite dimensional graded algebra which has the same generators and relations. As a byproduct, this gives a multiplicative structure on the homology groups of intervals of the NCP. Time permitting, I will talk about connections with the Milnor fibre of the corresponding reflection arrangement.