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arXiv · 1508.07449

Second homology of generalized periplectic Lie superalgebras

Zhihua Chang·Jin Cheng·Yongjie Wang
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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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Zhihua Chang, Jin Cheng, Yongjie Wang. 2018-01-25. Second homology of generalized periplectic Lie superalgebras. https://arxiv.org/abs/1508.07449

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