一类广义Kac-Moody代数的虚根系及由其特殊虚根决定的反射

RELATIONSHIP DETERMINED BY IMAGINARY ROOTS FOR A SPECIAL GKM ALGEBRA

我们知由虚根α决定的一类反射γα是属于有限维李代数g(A)的.若g(A)是可对称化的无限维李代数,那么我们就对它的每一个虚根α(虚根满足(α,α)<0)定义出一类反射γα,在此基础上.我们又讨论出这类Kac-Moody代数的严格虚根系、纯虚根系.

In this paper we give the imaginary root for a special GKM algebra at first. And then we give a definition for a special imaginary root. Also we get a relationship between reflections determinedly imaginary roots and the weyl group for the special GKM Algebra.