Twisted Hochschild Homology of Quantum Flag Manifolds: 2-Cycles from Invariant Projections

Abstract

We study the twisted Hochschild homology of quantum full ag manifolds, with the twist being the modular automorphism of the Haar state. We show that non-trivial 2cycles can be constructed from appropriate invariant projections. Moreover we show that HHθ 2(Cq[G/T]) has dimension at least rank(g). We also discuss the case of generalized ag manifolds and present the example of the quantum Grassmannians.