Finite-dimensional simple modules over certain iterated skew polynomial rings

DOI10.1016/0022-4049(95)90017-9zbMath0829.16017OpenAlexW2063862440MaRDI QIDQ1346814

David A. Jordan

Publication date: 17 January 1996

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(95)90017-9

zbMATH Keywords

quantum algebrasprimitive idealsenveloping algebrasaffine algebrasquantized Weyl algebrasfinite dimensional simple modules

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Ordinary and skew polynomial rings and semigroup rings (16S36) Universal enveloping (super)algebras (17B35) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Universal enveloping algebras of Lie algebras (16S30)

Related Items

Explicit representation theory of the quantum weyl algebra at roots of 1 ⋮ Adjoint functors raised from Ore extensions ⋮ Height one prime ideals of certain iterated skew polynomial rings ⋮ On the differential smoothness of 3-dimensional skew polynomial algebras and diffusion algebras ⋮ On weak annihilators and nilpotent associated primes of skew PBW extensions ⋮ On category \(\mathcal O\) over triangular generalized Weyl algebras. ⋮ Simple ambiskew polynomial rings. ⋮ On a class of iterated Ore extensions. ⋮ Irreducible Representations of the Quantum Weyl Algebra at Roots of Unity Given by Matrices ⋮ Invariants for automorphisms of certain iterated skew polynomial rings ⋮ Finite-dimensional simple Poisson modules ⋮ Down-up algebras ⋮ Down-up algebras and ambiskew polynomial rings ⋮ Finite-dimensional simple modules over quantised Weyl algebras ⋮ EXAMPLES OF FCR-ALGEBRAS ⋮ Isomorphism problems and groups of automorphisms for generalized Weyl algebras

Cites Work

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• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Prime ideals in skew polynomial rings and quantized Weyl algebras
• Iterated skew polynomial rings and quantum groups
• Height one prime ideals of certain iterated skew polynomial rings
• Prime ideals in skew and 𝑞-skew polynomial rings
• Lie superalgebras

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