Multiloop Lie algebras and the construction of extended affine Lie algebras
Multiloop Lie algebras and the construction of extended affine Lie algebras
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DOI：
10.1016/j.jalgebra.2010.01.029
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发表时间：
2008-07
期刊：
影响因子：
--
通讯作者：
Katsuyuki Naoi
中科院分区：
文献类型：
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作者：
Katsuyuki Naoi
我们知道，如果一个多圈李代数满足一定的条件，那么由多圈实现构造的多圈李代数可以是一个李Zn-环面，并且从一个李Zn-环面可以得到一族扩展仿射李代数（EALA）。然而，在许多情况下，即使一个给定的多圈李代数不满足这些条件，我们也可以由它构造一族EALA.本文研究了这一构造，证明了由两个多圈李代数构造的两族EALA在同构上重合当且仅当两个多圈李代数是“支撑同构”的.同时，给出了两个多圈李代数支撑同构的一个充要条件。
It is known that a multiloop Lie algebra, which is constructed using multiloop realization, can be a Lie Zn-torus if a given multiloop Lie algebra satisfies several conditions, and it is also known that a family of extended affine Lie algebras (EALAs) is obtained from a Lie Zn-torus. In many cases, however, even if a given multiloop Lie algebra does not satisfy these conditions, we can also construct a family of EALAs from it. In this paper, we study this construction, and prove that two families of EALAs constructed from two multiloop Lie algebras are coincide up to isomorphisms as EALAs if and only if two multiloop Lie algebras are “support-isomorphic”. Also, we give a necessary and sufficient condition for two multiloop Lie algebras to be support-isomorphic.