【摘要】：We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm|2n(R,-)that is coordinatized by an arbitrary unital associative superalgebra(R,-)with superinvolution.As a result,an identification between the second homology group of the Lie superalgebra ospm|2n(R,-)and the first skew-dihedral homology group of the associative superalgebra(R,-)with superinvolution is created for positive integers m and n with(m,n)=(1,1)and(m,n)=(2,1).The second homology groups of the Lie superalgebras osp1|2(R,-)and osp2|2(R,-)are also characterized explicitly.
[Abstract]:We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm|2n(R,-)that is coordinatized by an arbitrary unital associative superalgebra(R,-)with superinvolution.As a result,an identification between the second homology group of the Lie superalgebra ospm|2n(R,-)and the first skew-dihedral homology group of the associative superalgebra(R,-)with superinvolution is created for positive integers m and n with(m,n)=(1,1)and(m,n)=(2,1).The second homology groups of the Lie superalgebras osp1|2(R,-)and osp2|2(R,-)are also characterized explicitly.
【作者單位】： School
【基金】：supported by National Natural Science Foundation of China (Grant No. 11501213) the China Postdoctoral Science Foundation (Grant No. 2015M570705) the Fundamental Research Funds for the Central Universities (Grant No. 2015ZM085) the China Postdoctoral Science Foundation (Grant No. 2015M571928) the Fundamental Research Funds for the Central Universities
【分類號】：O152.5

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