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Second homology of generalized periplectic Lie superalgebras (1508.07449v3)

Published 29 Aug 2015 in math.RA

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 $\mathfrak{p}_m(R,{}-)$ 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 $\mathbb{Z}/2\mathbb{Z}$-graded dihedral homology of $R$ with certain superinvolution whenever $m\geqslant 5$.

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