The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3...The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered.展开更多
Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321： 3601-3619] constructed a new family of finite-dimensional modular Lie superalgebra Ω. Let Ω denote the even part of the Lie superalgebra Ω. We first give the gen...Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321： 3601-3619] constructed a new family of finite-dimensional modular Lie superalgebra Ω. Let Ω denote the even part of the Lie superalgebra Ω. We first give the generator sets of the Lie algebra Ω. Then, we reduce the derivation of Ω to a certain form. With the reduced derivation and a torus of Ω, we determine the derivation algebra of Ω.展开更多
In this article the ■-graded transitive modular Lie superalgebra ⊕_(i≥-1)L_i,whose repre- sentation of L_o in L_(-1)is isomorphic to the natural representation of osp(L_(-1)),is determined.
基金This work is partially supported by the National Natural Science Foundation of China(Grant No.10671160)China Postdoctoral Science Foundation(Grant No.20060400107)
文摘The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered.
文摘Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321： 3601-3619] constructed a new family of finite-dimensional modular Lie superalgebra Ω. Let Ω denote the even part of the Lie superalgebra Ω. We first give the generator sets of the Lie algebra Ω. Then, we reduce the derivation of Ω to a certain form. With the reduced derivation and a torus of Ω, we determine the derivation algebra of Ω.
基金Project supported by the NNSF (10271076)EMNSF (99036) of China
文摘In this article the ■-graded transitive modular Lie superalgebra ⊕_(i≥-1)L_i,whose repre- sentation of L_o in L_(-1)is isomorphic to the natural representation of osp(L_(-1)),is determined.
