arXiv subjects
Publications and source records attributed to Afsaneh Shamsaki.
In this paper, we define the non-commuting graph associated to a Lie algebra L and obtain some basic graph properties such as connectivity, diameter, girth, Hamiltonian and Eulerian. Moreover, planarity, outer planarity and isomorphism between two such graphs are also discussed in the paper.
In this paper, we introduce the commutativity degree of a finite-dimensional Lie algebra over a finite field and determine upper and lower bounds for it. Moreover, we study some relations between the notion of commutativity degree and known concepts in Lie algebras.
In this paper, the possible values of commutativity degree of Lie algebras are determined. Also, we define the asymptotic commutativity degree of Lie algebras and obtain the asymptotic commutativity degree for some of them. Moreover, we prove the existence of a family of Lie algebras such that the asymptotic commutativity degree is equal to 1\qk for all q greater than 2 and a positive integer k.
Let $L$ be an $(m\vert n)$-dimensional nilpotent Lie superalgebra where $m + n \geq 4$ and $n \geq 1$. This paper classifies such nilpotent Lie superalgebras $L$ with a derived subsuperalgebra of dimension $m+n-2$ such that $γ(L) = m + 2n - 2 - \dim \mathcal{M}(L)$, where $γ(L) \in \{0, 1, 2\}$ and $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Furthermore, we show that all these superalgebras are capable.
It is known that the dimension of the Schur multiplier of a non-abelian nilpotent Lie algebra $L$ of dimension $n$ is equal to $\frac{1}{2}(n-1)(n-2)+1-s(L)$ for some $ s(L)\geq0 $. The structure of all nilpotent Lie algebras has been given for $ s(L) \leq 4 $ in several papers. Here, we are going to give the structure of all non-abelian nilpotent Lie algebras for $s(L)=5$.
In this paper, we give the explicit structure of $ \otimes^{3} H $ and $ \wedge^{3} H $ where $ H $ is a generalized Heisenberg Lie algebra of rank at most $ 2. $ Moreover, for a non-abelian nilpotent Lie algebra $ L, $ we obtain an upper bound for the dimension of $ \otimes^{3} L.
The paper is devoted to obtain an upper bound for the Schur multiplier of nilpotent Lie algebras of maximal class. It improves the later upper bounds on the Schur multiplier of such Lie algebras.