arXiv subjects
Publications and source records attributed to Adel Alahmedi.
For a field $F$ of characteristic not 2 and a directed row-finite graph $Γ$ let $L(Γ)$ be the Leavitt path algebra with the standard involution $*.$ We study the Lie algebra $K=K(L(Γ),*)$ of $*-$skew-symmetric elements and find necessary and sufficient conditions for the Lie algebra $[K,K]$ to be simple.
Let $F$ be a field of characteristic not $2$ . An associative $F$-algebra $R$ gives rise to the commutator Lie algebra $R^{(-)}=(R,[a,b]=ab-ba).$ If the algebra $R$ is equipped with an involution $*:R\rightarrow R$ then the space of the skew-symmetric elements $K=\{a \in R \mid a^{*}=-a \}$ is a Lie subalgebra of $R^{(-)}.$ In this paper we find sufficient conditions for the Lie algebras $[R,R]$ and $[K,K]$ to be finitely generated.
We determine the structure of Leavitt path algebras of polynomial growth and discuss their automorphisms and involutions.
For a field $F$ and a row-finite directed graph $Γ$ let $L(Γ)$ be the Leavitt path algebra. We find necessary and sufficient conditions for the Lie algebra $[L(Γ),L(Γ)]$ to be simple.