Weight modules over infinite dimensional Weyl algebras

DOI10.1090/S0002-9939-2014-12071-5zbMath1331.17020arXiv1207.5780MaRDI QIDQ3190193

Dimitar Grantcharov, Volodymyr Mazorchuk, Vyacheslav M. Futorny

Publication date: 16 September 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.5780

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Infinite-dimensional Lie (super)algebras (17B65) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60)

Related Items (17)

Quantum affine modules for non-twisted Affine Kac-Moody algebras ⋮ Noncommutative fiber products and lattice models ⋮ Irreducible Witt modules from Weyl modules and \(\mathfrak{gl}_n\)-modules ⋮ Irreducible weight modules over the Schrödinger Lie algebra in \((n+1)\) dimensional space-time ⋮ The category of weight modules for symplectic oscillator Lie algebras ⋮ Bounded weight modules for basic classical Lie superalgebras at infinity ⋮ Bounded weight modules over the Lie superalgebra of Cartan \(W\)-type ⋮ Defining relations for minimal unitary quantum affine W-algebras ⋮ Classification of simple bounded weight modules of the Lie algebra of vector fields on \(\mathbb{C}^n\) ⋮ Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators ⋮ Simple bounded weight modules of \(\mathfrak{sl}(\infty)\), \(\mathfrak{o}(\infty)\), \(\mathfrak{sp}(\infty) \) ⋮ Classification of simple Harish-Chandra modules over the Neveu-Schwarz algebra and its contact subalgebra ⋮ Localization of free field realizations of affine Lie algebras ⋮ On fusion rules and intertwining operators for the Weyl vertex algebra ⋮ Representations of affine Lie superalgebras and their quantization in type \(A\) ⋮ On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebras ⋮ Simple weight modules over weak generalized Weyl algebras.

Cites Work

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• Affine Kac-Moody algebras and semi-infinite flag manifolds
• Fock space realizations of imaginary Verma modules
• Representations of affine Kac-Moody algebras, bosonization and resolutions
• Fock representations of the affine Lie algebra \(A_ 1^{(1)}\)
• Infinite tensor products of C*-algebras
• Classification of irreducible weight modules
• Characterization of Simple Highest Weight Modules
• Intermediate Wakimoto modules for affine
• Morita equivalence for rings with local units
• Indecomposable representations of generalized weyl algebras
• Semi-infinite induction and Wakimoto modules

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