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arXiv · 1807.11011

The capability and certain functors of some nilpotent Lie algebras of class two

Farangis Johari·Peyman Niroomand
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Abstract

Recently, the authors obtained the Schur multiplier, the non-abelian tensor square and the non-abelian exterior square of $d$-generator generalized Heisenberg Lie algebras of rank $ \frac{1}{2}d(d-1).$ Here, we intend to obtain the same results for $d$-generator generalized Heisenberg Lie algebras of rank $ t$ when $ \frac{1}{2}d(d-1)-3 \leq t\leq \frac{1}{2}d(d-1)-1.$ Then, as a result, we give similar consequences for a nilpotent Lie algebra $ L $ of class two when $ \dim (L/Z(L))=d,$ $ \dim L^2=t $ such that $ \frac{1}{2}d(d-1)-3 \leq t\leq \frac{1}{2}d(d-1)-1.$

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Farangis Johari, Peyman Niroomand. 2018-07-29. The capability and certain functors of some nilpotent Lie algebras of class two. https://doi.org/10.1080/03081087.2021.1983514

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