Simple weith modules over twisted generalized weyl algebras

DOI10.1080/00927879908826584zbMath0949.17003OpenAlexW2079545509MaRDI QIDQ4254193

Volodymyr Mazorchuk, Lyudmyla Turowska

Publication date: 2 September 1999

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879908826584

zbMATH Keywords

simple weight modulestwisted higher rank generalized Weyl algebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Ordinary and skew polynomial rings and semigroup rings (16S36) Rings of differential operators (associative algebraic aspects) (16S32) Ring-theoretic aspects of quantum groups (16T20)

Related Items (16)

Twisted generalized Weyl algebras and primitive quotients of enveloping algebras ⋮ Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras. ⋮ Noncommutative fiber products and lattice models ⋮ Grothendieck rings of towers of twisted generalized Weyl algebras ⋮ Duflo theorem for a class of generalized Weyl algebras ⋮ Grothendieck rings of towers of generalized Weyl algebras in the finite orbit case ⋮ Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators ⋮ Clifford and Weyl superalgebras and spinor representations ⋮ Multiparameter twisted Weyl algebras. ⋮ Locally finite simple weight modules over twisted generalized Weyl algebras. ⋮ Classification of twisted generalized Weyl algebras over polynomial rings ⋮ Cylindrical Dyck paths and the Mazorchuk-Turowska equation ⋮ Twisted Generalized Weyl Algebras, Polynomial Cartan Matrices and Serre-Type Relations ⋮ On the consistency of twisted generalized Weyl algebras ⋮ Simple weight modules over weak generalized Weyl algebras. ⋮ Fixed rings of twisted generalized Weyl algebras

Cites Work

• Unnamed Item
• Weight modules and their extensions over a class of algebras similar to the enveloping algebra of \(\mathfrak{sl}(2,\mathbb{C})\)
• Weight modules over generalized Weyl algebras
• A Class of Algebras Similar to the Enveloping Algebra of sl(2)

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