Irreducible Representations for the Baby Tits–Kantor–Koecher Algebra
Irreducible Representations for the Baby Tits–Kantor–Koecher Algebra
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DOI：
10.1080/00927870903049191
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发表时间：
2010-06
影响因子：
0.7
通讯作者：
Xiaoli Kong;Shaobin Tan
中科院分区：
文献类型：
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作者：
Xiaoli Kong;Shaobin Tan
由最小（非格）半格构造的Baby Tits-Kantor-Koecher（TKK）代数与有限维单李代数和仿射Kac-Moody代数以外的“最小”扩张仿射李代数有关.本文对婴儿TKK代数的有限维不可约表示进行了分类。事实证明，这样的表示可以从单李代数sp 4（n）的n个副本的直和的模中提升。
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).