Central extensions of generalized orthosymplectic Lie superalgebras

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• 作者：ZhiHua Chang ; YongJie Wang
• 关键词：orthosymplectic Lie superalgebra ; universal central extension ; ℤ/2ℤ-graded skew ; dihedral homology ; associative superalgebra with superinvolution
• 刊名：Science China Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：60
• 期：2
• 页码：223-260
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：60

文摘

We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra osp_m|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 osp_m|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 osp_1|2(R,-) and osp_2|2(R,-) are also characterized explicitly.