Multiloop realization of extended affine Lie algebras and Lie tori
Multiloop realization of extended affine Lie algebras and Lie tori
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DOI：
10.1090/s0002-9947-09-04828-4
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发表时间：
2007-09
影响因子：
1.3
通讯作者：
B. Allison;S. Berman;J. Faulkner;A. Pianzola
中科院分区：
文献类型：
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作者：
B. Allison;S. Berman;J. Faulkner;A. Pianzola
无限维李代数理论中的一个重要定理指出，任何仿射 Kac-Moody 代数都可以使用循环代数来实现（即显式构造）。在本文中，我们考虑一类李代数的相应问题，称为扩展仿射李代数（EALA），它概括了仿射代数。 EALA 出现在由无中心李环构造的族中，因此 EALA 的实现问题简化为无中心李环的实现问题。我们证明，除了一族之外的所有无心李环都可以使用多环代数（代替环代数）来实现。我们还获得了以这种方式实现的两个无心李托里是同位素的充分必要条件，这种关系对应于相应 EALA 族的同构关系。
An important theorem in the theory of infinite dimensional Lie algebras states that any affine Kac-Moody algebra can be realized (that is to say constructed explicitly) using loop algebras. In this paper, we consider the corresponding problem for a class of Lie algebras called extended affine Lie algebras (EALAs) that generalize affine algebras. EALAs occur in families that are constructed from centreless Lie tori, so the realization problem for EALAs reduces to the realization problem for centreless Lie tori. We show that all but one family of centreless Lie tori can be realized using multiloop algebras (in place of loop algebras). We also obtain necessary and sufficient conditions for two centreless Lie tori realized in this way to be isotopic, a relation that corresponds to isomorphism of the corresponding families of EALAs.