On the dimension of non-abelian tensor square of Lie superalgebras

2022/09/20 by Padhan, Rudra Narayan, Hasan, Ibrahem Yakzan, Pradhan, Sushree Sangeeta
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2209.09514

Abstract

In this paper, we determine upper bound for the non-abelian tensor product of finite dimensional Lie superalgebra. More precisely, if L is a non-abelian nilpotent Lie superalgebra of dimension (k | l) and its derived subalgebra has dimension (r | s), then dim (L⊗ L) ≤ (k+l-(r+s))(k+l-1)+2. We discuss the conditions when the equality holds for r=1, s=0 explicitly.

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