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 ...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.展开更多
文摘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.
