Second homology of generalized periplectic Lie superalgebras

2015/08/29 by Chang, Zhihua, Cheng, Jin, Wang, Yongjie
#17B05 #19D55 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1508.07449

Abstract

Let (R,^-) be an arbitrary unital associative superalgebra with superinvolution over a commutative ring \Bbbk with 2 invertible. The second homology of the generalized periplectic Lie superalgebra \mathfrakp_m(R,^-) for m\geqslant3 has been completely determined via an explicit construction of its universal central extension. In particular, this second homology could be identified with the first ℤ/2ℤ-graded dihedral homology of R with certain superinvolution whenever m\geqslant 5.

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