Infinite-dimensional 3-Lie algebras and their connections to Harish-Chandra modules

DOI10.1007/s11464-017-0606-7zbMath1419.17004arXiv1512.05843OpenAlexW2206774793MaRDI QIDQ2358365

Ruipu Bai, Zhenheng Li, Wei-Dong Wang

Publication date: 14 June 2017

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.05843

zbMATH Keywords

Witt algebratoroidal Lie algebraHarish-Chandra module3-Lie algebraintermediate series moduleinner derivation algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Infinite-dimensional Lie (super)algebras (17B65) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36) Ternary compositions (17A40)

Related Items (3)

The infinite dimensional unital Nambu–Poisson algebra of order 3 ⋮ Structure and cohomology of 3-Lie-Rinehart superalgebras ⋮ Structure on the simple canonical Nambu Rota-Baxter 3-Lie algebra \(A_{\partial}\)

Cites Work

• Toroidal Lie algebras and vertex representations
• The local structure of \(n\)-Poisson and \(n\)-Jacobi manifolds
• Vertex representations for \(n\)-toroidal Lie algebras and a generalization of the Virasoro algebra
• On foundation of the generalized Nambu mechanics
• Simple quotient algebras and subalgebras of Jacobian algebras
• Constructions of 3-Lie algebras
• Extended affine Lie algebras and their root systems
• Generalized Hamiltonian Dynamics
• On infinite-dimensional 3-Lie algebras
• Irreducible weight modules over Witt algebras
• Realizations of 3-Lie algebras
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