On certain Hochschild cohomology groups for the small quantum group

Abstract

We apply the sheaf cohomology BGG method developed by the authors and Lachowska-Qi to the computation of Hochschild cohomology groups of various blocks of the small quantum group. All our computations of the center of the corresponding block agree with the conjectures of Lachowska-Qi. In the case of the nontrivial singular block for $\mathfrak{g}={\mathfrak{sl}}_3$, we obtain the H*$(\mathfrak{u},\mathbb{C})=\mathbb{C}[\mathcal{N}]$-module structure of HH*$({\mathfrak{u}}_{\lambda })$.

25 pages, 34 figures

References in corpus (3)

• The center of small quantum groups I: the principal block in type A
• The center of the small quantum group II: singular blocks
• A computer algorithm for the BGG resolution