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首页> 外文期刊>Canadian Journal of Mathematics >Generalized Reductive Lie Algebras: Connections With Extended Affine Lie Algebras and Lie Tori
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Generalized Reductive Lie Algebras: Connections With Extended Affine Lie Algebras and Lie Tori

机译：广义归约李代数：与扩展仿射李代数和李托里的联系

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摘要

We investigate a class of Lie algebras which we call {it generalized reductiveLie algebras}. These are generalizations of semi-simple, reductive, and affineKac--Moody Lie algebras. A generalized reductive Lie algebra which has an irreducibleroot system is said to be {it irreducible/} and we note that this class of algebrashas been under intensive investigation in recent years. They have also been called{it extended affine Lie algebras}. The larger class of generalized reductive Liealgebras has not been so intensively investigated. We study them in this paper and notethat one way they arise is as fixed point subalgebras of finite order automorphisms. Weshow that the core modulo the center of a generalized reductive Lie algebra is a directsum of centerless Lie tori. Therefore one can use the results known about theclassification of centerless Lie tori to classify the cores modulo centers ofgeneralized reductive Lie algebras.
机译：我们研究了一类李代数，我们称其为{广义广义归纳代数}。这些是半简单，归约和仿射Kac-Moody Lie代数的推广。具有不可约根系统的广义归一化李代数据说是{it irreducible /}，我们注意到近年来这类代数正在深入研究中。它们也被称为{它的扩展仿射李代数}。对广义归一化还原Liealgebras的更大类别尚未进行如此深入的研究。我们在本文中对它们进行了研究，并注意到它们出现的一种方式是作为有限阶自同构的不动点子代数。我们表明，广义归约李代数中心的模核是无心李托里的正和。因此，人们可以利用关于无心李氏托里分类的已知结果来归纳广义归一化李李代数的模中心。

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