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arXiv · 1512.05843

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

Ruipu Bai·Zhenheng Li·Weidong Whang
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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.

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Ruipu Bai, Zhenheng Li, Weidong Whang. 2015-12-18. Infinite Dimensional 3-Lie Algebras and Their Connections to Harish-Chandra Modules. https://arxiv.org/abs/1512.05843

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