| Relationship between Reflections Determined by Imaginary Roots and the Weyl Group for a Special GKM Algebra |
| Received:July 22, 1996 |
| Key Words:
generalized Kac-Moody algebra imaginary root system the Weyl group special imaginary root
|
| Fund Project:NNSF of China and NSF of Hebei Province |
|
| Hits: 2564 |
| Download times: 1074 |
| Abstract: |
| 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 roots of a class of rank 3 GKM algebras. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1999.03.006 |
| View Full Text View/Add Comment |
