Twisted Hochschild homology of quantum flag manifolds: 2-cycles from invariant projections

摘要

We study the twisted Hochschild homology of quantum full flag manifolds, with the twist being the modular automorphism of the Haar state. We show that nontrivial 2-cycles can be constructed from appropriate invariant projections. Moreover, we show that HH2 theta(C-q[G/T]) has dimension at least rank(g). We also discuss the case of generalized flag manifolds and present the example of the quantum Grassmannians.