Locally loop algebras and locally affine Lie algebras

被引：6

作者：

Morita, Jun ^{[1
]}

Yoshii, Yoji ^{[2
]}

机构：

[1] Univ Tsukuba, Inst Math, Tsukuba, Ibaraki 3058571, Japan

[2] Iwate Univ, Morioka, Iwate 0208550, Japan

来源：

JOURNAL OF ALGEBRA | 2015年 / 440卷

关键词：

Lie algebras; Affine Lie algebras; Loop algebra; Root systems; Locally finite split simple Lie algebras; INVARIANT FORMS; ROOT SYSTEMS; DERIVATIONS;

D O I：

10.1016/j.jalgebra.2015.05.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this study, we investigate a new class of Lie algebras, i.e., tame locally extended affine Lie algebras of nullity 1, which are an infinite-rank analog of affine Lie algebras. This type of algebra is called a locally affine Lie algebra. A certain ideal of a locally affine Lie algebra, called a core, is a universal extension of a local version of a loop algebra, which is called a locally loop algebra. We classify locally loop algebras and locally affine Lie algebras. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：379 / 442

页数：64

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