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Original Articles

Representations of Vector Product n-Lie Algebras

Pages 3315-3326 | Received 01 Oct 2002, Accepted 01 Jan 2004, Published online: 01 Feb 2007
 

Abstract

Let V n  = ⟨e 1,…, e n+1⟩ be the vector product n-Lie algebra with n-Lie commutator [e 1,…, ˆe i ,…, e n+1] = (− 1) i e 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 an n-Lie extension of s o n+1-module with highest weight tπ1 for some nonnegative integer t.

1991 Mathematics Subject Classification:

Acknowledgments

I am grateful to INTAS foundation for support. I am thankful to referee for paying of my attention to the preprint Sh. M. Kasymov, E. N. Kuz'min, “Classification of representations of split simple n-Lie algebra of type A 1”, preprint No. 23, IM SO RAN, Novosibirsk, 1987, where was obtained results similar to ours.

Notes

#Communicated by I. Shestakov.

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