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 non-trivial 2-cycles can be constructed from appropriate invariant projections. The main result is that $H{H}_2^{\theta }({\mathbb{C}}_q[G/T])$ is infinite-dimensional when $\mathrm{rank}(\mathfrak{g})>1$. We also discuss the case of generalized flag manifolds and present the example of quantum Grassmannians.

v2: one result weakened, some rewriting

References in corpus (3)

• Twisted cyclic homology of all Podles quantum spheres
• Hopf Algebra Equivariant Cyclic Cohomology, K-theory and Index Formulas
• Twisted Homology of Quantum SL(2) - Part II