A Parametric Family of Subalgebras of the Weyl Algebra II. Irreducible Modules

zbMath1308.16022arXiv1212.1404MaRDI QIDQ4981390

Samuel A. Lopes, Matthew Ondrus, Georgia M. Benkart

Publication date: 24 June 2014

Full work available at URL: https://arxiv.org/abs/1212.1404

zbMATH Keywords

automorphism groupsquantum Weyl algebrasdifferential operatorsirreducible modulesalgebras of invariantsOre extensionsquantum planes

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Automorphisms and endomorphisms (16W20) Rings of differential operators (associative algebraic aspects) (16S32) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

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Isomorphism problems and groups of automorphisms for Ore extensions 𝐾[𝑥[𝑦;𝛿] (zero characteristic)] ⋮ Symplectic reflection algebras in positive characteristic as Ore extensions ⋮ THE PRIME IDEALS AND SIMPLE MODULES OF THE UNIVERSAL ENVELOPING ALGEBRA U(𝔟⋉V₂) ⋮ Normally ordered forms of powers of differential operators and their combinatorics ⋮ Actions of the additive group \(G_a\) on certain noncommutative deformations of the plane ⋮ A unified algebraic underpinning for the Hahn polynomials and rational functions ⋮ Derivations of a parametric family of subalgebras of the Weyl algebra. ⋮ Identities for a parametric Weyl algebra over a ring ⋮ A parametric family of subalgebras of the Weyl algebra I. Structure and automorphisms ⋮ Identities for subspaces of a parametric Weyl algebra

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