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Representations of n-Lie algebras

A. S. Dzhumadil'daev
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Abstract

Let $V_n= $ be a vector products n-Lie algebra with n-Lie commutator $[e_1,...,\hat{e_i},...,e_{n+1}]=(-1)^ie_i$ over the field of complex numbers. Any finite-dimensional n-Lie $V_n$-module is completely reducible. Any finite-dimensional irreducible n-Lie $V_n$-module is isomorphic to a n-Lie extension of $so_{n+1}$-module with highest weight $tπ_1$ for some nonnegative integer t.

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BibTeXRIS

A. S. Dzhumadil'daev. 2002-02-05. Representations of n-Lie algebras. https://arxiv.org/abs/math/0202041

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