Infinite Dimensional 3-Lie Algebras and Their Connections to Harish-Chandra Modules

2015/12/18 by Bai, Ruipu, Li, Zhenheng, Whang, Weidong · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1512.05843

Abstract

In this paper we construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation algebras. In particular, for the second kind of 3-Lie algebras, we find that their regular representations are Harish-Chandra modules, and the inner derivation algebras give rise to intermediate series modules of the Witt algebras and contain the smallest full toroidal Lie algebras without center.

Cited by

• Transposed Poisson Structures on Two Nambu 3-Lie Algebras

Related

• The infinite dimensional Unital 3-Lie Poisson algebra
• Weil Algebra, 3-Lie Algebra and B.R.S. Algebra
• On Nambu-Lie 3-algebra representations
• Constructing 3-Lie algebras
• 3-Lie algebra A_ω^δ-modules and induced modules