Generalized Weyl algebras and diskew polynomial rings

DOI10.1142/S0219498820501947zbMath1464.16018arXiv1612.08941OpenAlexW2973088661WikidataQ114614555 ScholiaQ114614555MaRDI QIDQ5133843

Vladimir V. Bavula

Publication date: 11 November 2020

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.08941

zbMATH Keywords

localizationsimple modulegeneralized Weyl algebratorsion modulediskew polynomial rings

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Ideals in associative algebras (16D25) Universal enveloping algebras of Lie algebras (16S30) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items (4)

Description of bi-quadratic algebras on 3 generators with PBW basis ⋮ The Heisenberg double of the quantum Euclidean group and its representations ⋮ On the augmentation topology of automorphism groups of affine spaces and algebras ⋮ The global dimension of the generalized Weyl algebras 𝑆⁻¹𝐾[𝐻,𝐶[𝑋,𝑌;𝜎,𝑎]]

Cites Work

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• Classification of simple sl(2)-modules and finite-dimensionality of the module of extensions of simple sl(2)-modules
• Finite dimensionality of \(\text{Ext}^ n\)'s and \(\text{Tor}_ n\)'s of simple modules over one class of algebras
• Iterated skew polynomial rings and quantum groups
• Description of two-sided ideals in a class of noncommutative rings. I
• Description of two-sided ideals in a class of noncommutative rings. II
• Extreme modules over the Weyl algebra \(A_ n\)
• Simple ambiskew polynomial rings.
• Simple D[X, Y; ?,a-modules]
• A Class of Algebras Similar to the Enveloping Algebra of sl(2)
• Dimension, multiplicity, holonomic modules, and an analogue of the inequality of Bernstein for rings of differential operators in prime characteristic
• Invariants for automorphisms of certain iterated skew polynomial rings
• Filter dimension of algebras and modules, a simplicity criterion of generalized weyl algebras

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