Hochschild homology and cohomology of Generalized Weyl algebras: the quantum case
Andrea Solotar, Mariano Su\'arez-Alvarez, Quimey Vivas
TL;DR
This paper computes the Hochschild homology and cohomology for quantum-type generalized Weyl algebras of rank one, providing a comprehensive understanding of their algebraic invariants.
Contribution
It determines the Hochschild homology and cohomology for a broad class of quantum generalized Weyl algebras, extending previous results to most cases.
Findings
Hochschild homology and cohomology are explicitly calculated for quantum generalized Weyl algebras.
Results cover all but a few exceptional cases of these algebras.
Provides a foundation for further algebraic and representation-theoretic studies.
Abstract
We determine the Hochschild homology and cohomology of the generalized Weyl algebras of rank one which are of 'quantum' type in all but a few exceptional cases.
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