Capability of Nilpotent Lie Superalgebras of Small Dimension
In this paper, we define partially capable Lie superalgebra. As an application we classify all capable nilpotent Lie superalgebras of dimension less than equal to five.
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arXiv subjects
Ibrahem Yakzan Hasan
Publications and source records attributed to Ibrahem Yakzan Hasan.
On the dimension of the Schur multiplier of nilpotent Lie superalgebras
We provide a bound on the dimension of Schur multiplier of a finite dimensional nilpotent Lie superalgebra which is more precise than the previous bounds on the dimension of Schur multiplier of Lie superalgebra.
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Finite-dimensional nilpotent Lie superalgebras of class two and skew-supersymmetric bilinear maps
In this article, we discuss the category $\mathcal{SN}_2$ where the objects are finite-dimensional nilpotent Lie superalgebras of class two and the category $\mathcal{SSKE}$ where the objects are skew-supersymmetric bilinear maps. We establish relation between $\mathcal{SN}_2$ and $\mathcal{SSKE}$. As a result, we discuss the capability of nilpotent Lie superalgebras of class two.
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On the triple tensor product of generalized Heisenberg Lie superalgebra of rank $\leq2$
In this article, we compute the Schur multiplier of all generalized Heisenberg Lie superalgebras of rank $2$. We discuss the structure of $\otimes^3H$ and $\wedge^3H$ where $H$ is a generalized Heisenberg Lie superalgebra of rank $\leq2$. Moreover, we prove that if $L$ is an $(m\mid n)$-dimensional non-abelian nilpotent Lie superalgebra with derived subalgebra of dimension $(r\mid s)$, then $\dim\otimes^3L \leq (m+n)(m+n - (r+s))^2$. In particular, for $r=1,s=0$ the equality holds if and only if $L \cong H(1\mid 0)$.
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On the dimension of non-abelian tensor square of Lie superalgebras
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 $(k \mid l)$ and its derived subalgebra has dimension $(r \mid s)$, then $ \dim (L\otimes L) \leq (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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Detecting capable pairs of some nilpotent Lie superalgebras
In this article, we define the capable pairs of Lie superalgebras. We classify all capable pairs of abelian and Heisenberg Lie superalgebras. After that we discuss on pairs of Lie superalgebras with derived subalgebra of dimension one and a non-abelian ideal. Finally, we determine the structure of the Schur multiplier of pairs of Heisenberg Lie superalgebras.
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