On certain Hochschild cohomology groups for the small quantum group

DOI10.1016/J.JALGEBRA.2022.04.034arXiv2104.05113MaRDI QIDQ6365027

Publication date: 11 April 2021

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

m a t h f r a k g = m a t h f r a k {s l}_{3}

, we obtain the H*

(m a t h f r a k u, m a t h b b C) = m a t h b b C [m a t h c a l N]

-module structure of HH*

(m a t h f r a k u_{l a m b d a})

.

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Cohomology of Lie (super)algebras (17B56) Computational methods for problems pertaining to nonassociative rings and algebras (17-08) Software, source code, etc. for problems pertaining to nonassociative rings and algebras (17-04)

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