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Original Articles

Irreducible Representations for the Baby Tits–Kantor–Koecher Algebra

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Pages 2177-2183 | Received 07 Dec 2008, Published online: 14 Jun 2010
 

Abstract

The baby Tits–Kantor–Koecher (TKK) algebra constructed from the smallest (nonlattice) semilattice is related to the “smallest” extended affine Lie algebras other than the finite dimensional simple Lie algebras and the affine Kac–Moody algebras. In this article, we classify the finite dimensional irreducible representations for the baby TKK algebra. It turns out that such representations can be lifted from modules of direct sums of finitely many copies of the simple Lie algebra sp 4(ℂ).

2000 Mathematics Subject Classification:

ACKNOWLEDGMENT

This article is supported by the National Natural Science Foundation of China (No. 10931006).

Notes

Communicated by K. Misra.

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