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Representations of n-Lie algebras
Representations of n-Lie algebras
2002-02-05
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arxiv.org/abs/math/0202041v1
Mathematics
Representation Theory
16 pages, LaTeX
Scientific paper
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 $t\pi_1$ for some nonnegative integer t.
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