一类Block型李超代数的超导子
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摘要
构造了一类Block型李超代数.主要研究了Block型李超代数SB(2~(1/2))的超导子代数和一阶上同调群,给出了李超代数SB(2~(1/2))超导子结构,指出其一阶上同调群是非平凡的.
A new class of Lie superalgebras of Block type have been constructed.The study is mainly focused on its superderivations and the first cohomology group.The structure of superderivation of SB(2~(1/2))is given.It is proved that the first cohomology group of SB(2~(1/2))is nontrivial.
A new class of Lie superalgebras of Block type have been constructed.The study is mainly focused on its superderivations and the first cohomology group.The structure of superderivation of SB(2~(1/2))is given.It is proved that the first cohomology group of SB(2~(1/2))is nontrivial.
引文
[1] CHENG S J,KAC V G.Structure of some Z-graded Lie superalgebras of vector fields[J].Transformation Groups,1999,4(2/3):219-272.
[2] ZHANG R B,CHENG S J.Howe duality and combinatorial Characyer formula for orthosymplectic Lie superalgebras[J].Advances in Mathematics,2004,182(1):124-172.
[3] SU Y C.Classification of finite-dimensional modules of singly atypical type over the Lie superalgebras sl(m,n)[J].Journal of Mathematical Physics,2000,41(1):602-613.
[4] SCHEUNERT M.The theory of Lie superalgebras[M].Berlin:Springer-Verlag,1979:1-270
[5] KAC V G.Characters of typical representations of classical Lie superalgebras[J].Communications in Algebra,1977,5(8):889-897.
[6] KAC V G.Classification of infinite-dimensional simple linearly compact Lie superalgebras[J].Advances in Mathematics,1998,139(1):1-55.
[7] SU Y C.Classification of finite-dimensional modules of the Lie superalgebra sl(2|1)[J].Communications in Algebra,1992,20:3259-3277.
[8] KAC V G.Lie superalgebras[J].Advances in Mathematics,1977,26(1):8-96.
[9]张永正,刘文德.模李超代数[M].北京:科学出版社,2004:1-186.
[10]夏春光.一类非有限Z-分次Block型李代数[D].合肥:中国科学技术大学,2013.
[11]苏育才.有限维半单李代数的简明教程[M].北京:科学出版社,2014:35-37.
[12]白薇.Cartan型李超代数的超导子与极大子代数[D].哈尔滨:哈尔滨工业大学,2014.
[2] ZHANG R B,CHENG S J.Howe duality and combinatorial Characyer formula for orthosymplectic Lie superalgebras[J].Advances in Mathematics,2004,182(1):124-172.
[3] SU Y C.Classification of finite-dimensional modules of singly atypical type over the Lie superalgebras sl(m,n)[J].Journal of Mathematical Physics,2000,41(1):602-613.
[4] SCHEUNERT M.The theory of Lie superalgebras[M].Berlin:Springer-Verlag,1979:1-270
[5] KAC V G.Characters of typical representations of classical Lie superalgebras[J].Communications in Algebra,1977,5(8):889-897.
[6] KAC V G.Classification of infinite-dimensional simple linearly compact Lie superalgebras[J].Advances in Mathematics,1998,139(1):1-55.
[7] SU Y C.Classification of finite-dimensional modules of the Lie superalgebra sl(2|1)[J].Communications in Algebra,1992,20:3259-3277.
[8] KAC V G.Lie superalgebras[J].Advances in Mathematics,1977,26(1):8-96.
[9]张永正,刘文德.模李超代数[M].北京:科学出版社,2004:1-186.
[10]夏春光.一类非有限Z-分次Block型李代数[D].合肥:中国科学技术大学,2013.
[11]苏育才.有限维半单李代数的简明教程[M].北京:科学出版社,2014:35-37.
[12]白薇.Cartan型李超代数的超导子与极大子代数[D].哈尔滨:哈尔滨工业大学,2014.