Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.
This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a du...This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a duality between these homology groups and the simplicial homology groups of K.展开更多
First, the authors give a GrSbner-Shirshov basis of the finite-dimensional irre- ducible module Vq（λ） of the Drinfeld-Jimbo quantum group Uq（G2） by using the double free module method and the known GrSbner-Shirsh...First, the authors give a GrSbner-Shirshov basis of the finite-dimensional irre- ducible module Vq（λ） of the Drinfeld-Jimbo quantum group Uq（G2） by using the double free module method and the known GrSbner-Shirshov basis of Uq（G2）. Then, by specializing a suitable version of Uq （G2） at q = 1, they get a GrSbner-Shirshov basis of the universal enveloping algebra U（G2） of the simple Lie algebra of type G2 and the finite-dimensional irreducible U（G2）-module V（λ）.展开更多
For a graded simple Lie algebra of Cartan type L=X(m:n) (2) X∈{W,S,H,K} , over a field F of odd characteristic p , the group generated by one-parameter subgroups of the form exp( t ad y )is descr...For a graded simple Lie algebra of Cartan type L=X(m:n) (2) X∈{W,S,H,K} , over a field F of odd characteristic p , the group generated by one-parameter subgroups of the form exp( t ad y )is described, where y∈L+F u satisfying y p=0 , t∈F and u is some fixed element of the p -envelope of L in Der u (m :n).展开更多
基金supported by National Natural Science Foundation of China (Grant No.10771182)Doctorate Foundation Ministry of Education of China (Grant No. 200811170001)
文摘Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.
基金supported by the National Natural Science Foundation of China(Nos.11371093,11261062,11471167)
文摘This paper deals with homology groups induced by the exterior algebra generated by the simplicial compliment of a simplicial complex K. By using ech homology and Alexander duality, the authors prove that there is a duality between these homology groups and the simplicial homology groups of K.
基金supported by the National Natural Science Foundation of China(Nos.11061033,11361056)
文摘First, the authors give a GrSbner-Shirshov basis of the finite-dimensional irre- ducible module Vq（λ） of the Drinfeld-Jimbo quantum group Uq（G2） by using the double free module method and the known GrSbner-Shirshov basis of Uq（G2）. Then, by specializing a suitable version of Uq （G2） at q = 1, they get a GrSbner-Shirshov basis of the universal enveloping algebra U（G2） of the simple Lie algebra of type G2 and the finite-dimensional irreducible U（G2）-module V（λ）.
文摘For a graded simple Lie algebra of Cartan type L=X(m:n) (2) X∈{W,S,H,K} , over a field F of odd characteristic p , the group generated by one-parameter subgroups of the form exp( t ad y )is described, where y∈L+F u satisfying y p=0 , t∈F and u is some fixed element of the p -envelope of L in Der u (m :n).
