Relationship between Reflections Determined by Imaginary Roots and the Weyl Group for a Special GKM Algebra  

一类特殊广义Kac-Moody代数虚根决定的反射与Weyl群间的关系(英)

作　　者：李振亨[1] 靳一东[2] 白瑞蒲[1] 

机构地区：[1]河北大学数学系,保定071002 [2]华北电力大学基础科学系,保定071003

出　　处：《Journal of Mathematical Research and Exposition》1999年第3期501-507,共7页数学研究与评论（英文版）

摘　　要：It's well known that a reflectin rα associated to every root α belongs to the Weyi group of a Lie algebra g(A) of finite type. When g(A) is a symmetrizable Kac-Moody algebra of indefinite type, one of can define a reflection rα for every imzginary root α satisfying (α, α) < 0. From [3] we know rα ∈-W or rα is an element of-W mutiplied by a diagram automorphism . How about the relationship between reflections associated to imaginary root and the Weyl group of a symmetrized Kac-Moody algebra (GKM algebra for short)? We shall discuss it for a special GKM algebra in present paper (see 3). In sections 1 and 2 we introduce some basic concepts and give the set of imaginary root of a class of rand 3 GKM algebras.对有限型李代数g（A），相应于每个根α的反射rα均在g（A）的Weyl群W中．当g（A）为可对称化的不定型Kac－Moody代数时，若α为一虚根且（α，α）＜0，则亦可定义反射rα并有rα∈－W或rα是－W中元与一个图自同构之积（见[3]）．本文给出了一类秩为3的广义Kac－Moody代数的虚根系，然后讨论了一类特殊的广义Kac－Moody代数的虚根决定的反射与Weyl群之间的关系．

关 键 词：generalized Kac-Moody algebra imaginary root system the Weyl group special imaginary root 

分 类 号：O152.5[理学—数学]