Self-dual Nichols-Woronowicz algebras and cohomology of flag manifolds

Nichols-Woronowicz algebras are Hopf algebras in nonsymmetric tensor categories, which have recently attracted considerable interest. In my talk, I will describe a self-dual Nichols-Woronowicz algebra B(W) associated to a given Coxeter group W, and will show that both the nilCoxeter algebra of W and the coinvariant algebra of W are contained in B(W). There is also a `quantum' version of this result for crystallographic Coxeter groups.