Algebra Seminar: Zhang -- Noncrossing algebras associated to finite Coxeter groups

Yang Zhang (University of Sydney) 

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

Title: Noncrossing algebras associated to finite Coxeter groups 

Abstract: 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.