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

Abstract

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 [Formula: see text]-cycles can be constructed from appropriate invariant projections. Moreover, we show that [Formula: see text] has dimension at least rank [Formula: see text]. We also discuss the case of generalized flag manifolds and present the example of the quantum Grassmannians.