A class of new simple modules for \(\mathfrak{sl}_{n + 1}\) and the Witt algebra

DOI10.1016/j.jalgebra.2019.09.011zbMath1469.17006OpenAlexW2975436533MaRDI QIDQ2330321

Yan He, Yan-an Cai, Rencai Lü

Publication date: 28 October 2019

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2019.09.011

zbMATH Keywords

free modulessimple modulesWitt algebranon-weight modules\(\mathfrak{sl}_{n + 1}\)

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Virasoro and related algebras (17B68) Lie algebras of vector fields and related (super) algebras (17B66) Infinite-dimensional Lie (super)algebras (17B65) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (6)

A class of non-weight modules of \(U_p(\mathfrak{s} \mathfrak{l}_2)\) and Clebsch-Gordan type formulas ⋮ Module structures on \(U(S^-)\) for the Schrödinger algebra ⋮ Non-weight representations of Lie superalgebras of Block type. II ⋮ Irreducible \(Y(\mathfrak{gl}_{n+1})\)-module structures on a commutative subalgebra ⋮ Non-weight representations of Lie superalgebras of block type. I ⋮ Exponentiation and Fourier transform of tensor modules of \(\mathfrak{sl}(n+1)\)

Cites Work

• Unnamed Item
• Unnamed Item
• Irreducible Virasoro modules from tensor products
• Classification of irreducible representations of Lie algebra of vector fields on a torus
• Irreducible Virasoro modules from irreducible Weyl modules
• Classification of simple weight Virasoro modules with a finite-dimensional weight space
• \(\mathcal{U}(\mathfrak{h})\)-free modules and coherent families
• Categorification of (induced) cell modules and the rough structure of generalised Verma modules
• On modules induced from Whittaker modules
• Classification of Harish-Chandra modules over the Virasoro Lie algebra
• On Whittaker vectors and representation theory
• A class of representations over the Virasoro algebra
• Irreducible modules over Witt algebras \(\mathcal {W}_{n}\) and over \(\mathfrak {sl}_{n+1}(\mathbb {C})\)
• Generalized Verma modules over \(\mathfrak{sl}_{n + 2}\) induced from \(\mathcal{U}(\mathfrak{h}_n)\)-free \(\mathfrak{sl}_{n + 1}\)-modules
• Verma modules over generalized Virasoro algebras Vir[\(G\)]
• Irreducible representations of the Lie-algebra of the diffeomorphisms of a \(d\)-dimensional torus
• Classification of irreducible weight modules
• Irreducible Virasoro modules from tensor products. II
• A family of simple weight modules over the Virasoro algebra
• Simple Virasoro modules which are locally finite over a positive part
• Simple \(\mathfrak{sl}_{n + 1}\)-module structures on \(\mathcal{U}(\mathfrak{h})\)
• \(\mathcal{W}_n^+\)- and \(\mathcal{W}_n\)-module structures on \(U(\mathfrak{h}_n)\)
• A class of simple weight Virasoro modules
• Tensor product weight modules over the Virasoro algebra
• Supports of weight modules over Witt algebras
• New irreducible weight modules over Witt algebras with infinite-dimensional weight spaces
• WHITTAKER MODULES FOR THE VIRASORO ALGEBRA
• Partial classification of modules for Lie-algebra of diffeomorphisms of d-dimensional torus
• Simple Witt modules that are finitely generated over the cartan subalgebra
• A Module Induced from a Whittaker Module
• Generalized Verma modules induced from \(sl(2,\mathbb{C})\) and associated Verma modules

This page was built for publication: A class of new simple modules for \(\mathfrak{sl}_{n + 1}\) and the Witt algebra