Central extensions of generalized orthosymplectic Lie superalgebras

2015/09/02 by Zhihua Chang, Yongjie Wang, Chang, Zhihua +1
Mathematics · Physics and Astronomy · #17B05 #19D55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1509.00572

openalex publication_date 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The key ingredient of this paper is the universal central extension of the generalized orthosymplectic Lie superalgebra \mathfrakosp_m|2n(R,^-) coordinatized by a unital associative superalgebra (R,^-) with superinvolution. Such a universal central extension will be constructed via a Steinberg orthosymplectic Lie superalgebra coordinated by (R,^-). The research on the universal central extension of \mathfrakosp_m|2n(R,^-) will yield an identification between the second homology group of the generalized orthosymplectic Lie superalgebra \mathfrakosp_m|2n(R,^-) and the first ℤ/2ℤ-graded skew-dihedral homology group of (R,^-) for (m,n)≠(2,1),(1,1). The universal central extensions of \mathfrakosp_2|2(R,^-) and \mathfrakosp_1|2(R,^-) will also be treated separately.

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