Locally finite simple weight modules over twisted generalized Weyl algebras

Abstract

We present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. When a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification of a class of locally finite simple weight modules as those induced from simple modules over a subalgebra isomorphic to a tensor product of noncommutative tori. As an application we describe simple weight modules over the quantized Weyl algebra.

28 pages

Cited by in corpus (18)

• The algebra of integro-differential operators on a polynomial algebra
• Multiparameter Twisted Weyl Algebras
• On the Consistency of Twisted Generalized Weyl Algebras
• Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras
• The isomorphism problem for multiparameter quantized Weyl algebras
• Twisted generalized Weyl algebras, polynomial Cartan matrices and Serre-type relations
• Twisted generalized Weyl algebras and primitive quotients of enveloping algebras
• Noncommutative fiber products and lattice models
• Cylindrical Dyck paths and the Mazorchuk-Turowska equation
• Classification of twisted generalized Weyl algebras over polynomial rings
• Fixed rings of twisted generalized Weyl algebras
• Clifford and Weyl superalgebras and spinor representations
• Twisted Weyl algebras, crossed products, and representations
• Simple weight modules over weak Generalized Weyl algebras
• On rational twisted generalized Weyl algebra
• The group of automorphisms of the Jacobian algebra $\mA_n$
• Explicit description of generalized weight modules of the algebra of polynomial integro-differential operators $I_n$
• Weight modules of quantized Weyl algebras