泛阶化李超代数

Universal Graded Lie Superalgebras

对于给定的负阶化李超代数K-,本文定义了K-型泛阶化李超代数并证明了它的存在性．进而引出阶化Cartan型李超代数,并且证得阶化Cartan型李超代数 W(m,n),K(m,n,ωA),S(m,n)和H(m,n)分别可以用某种泛阶化李超代数来刻画．

For a given negatively graded Lie superalgebra K^-, the universal graded Lie superalgrbras U of type K^- is defined and its existence is proved. By posing additional conditions on K^-, other types of uaiversal graded Lie superalgebras are defined and discussed. The concept of universal graded Lie superalgebras leads naturally to the graded Cartan type Lie superalgebras, and it is proved that the graded Cartan type Lie superalgerbras K（m, n, wA）, S（m, n） and H（m, n） can be characterized as certain universal graded Lie superalgebras.