The convex PBW-type Lyndon basis for two-parameter quantum group U_(r,s)(F_(4))is given.Assume thatrs^(-1)is a primitive l-th root of unity with l odd,then the restricted quantum group u_(r,s)(F_(4))as a quotient of U...The convex PBW-type Lyndon basis for two-parameter quantum group U_(r,s)(F_(4))is given.Assume thatrs^(-1)is a primitive l-th root of unity with l odd,then the restricted quantum group u_(r,s)(F_(4))as a quotient of U_(r,s)(F_(4))is pointed,and of a Drinfel’d double structure under a certain condition.All of Hopf isomorphisms of u_(r,s)(F_(4))are determined,and the necessary and sufficient condition for u_(r,s)(F_(4))to be a ribbon Hopf algebra is singled out by describing the left and right integrals.展开更多
For exceptional Lie superalgebras D（2, 1; α）, G（3） and F（4）, GrSbner-Shirshov bases and the corresponding super-Lyndon-Shirshov monomial bases are constructed.
基金Nai Hong Hu is supported by the NNSF of China(Grant Nos.12171155,12071094)in part by Science and Technology Commission of Shanghai Municipality(Grant No.22DZ2229014)。
文摘The convex PBW-type Lyndon basis for two-parameter quantum group U_(r,s)(F_(4))is given.Assume thatrs^(-1)is a primitive l-th root of unity with l odd,then the restricted quantum group u_(r,s)(F_(4))as a quotient of U_(r,s)(F_(4))is pointed,and of a Drinfel’d double structure under a certain condition.All of Hopf isomorphisms of u_(r,s)(F_(4))are determined,and the necessary and sufficient condition for u_(r,s)(F_(4))to be a ribbon Hopf algebra is singled out by describing the left and right integrals.
文摘For exceptional Lie superalgebras D（2, 1; α）, G（3） and F（4）, GrSbner-Shirshov bases and the corresponding super-Lyndon-Shirshov monomial bases are constructed.
