Главная

Gene Abrams

  1. Isomorphism and Morita equivalence of graph algebras.

    Ср, 12/09/2009 - 16:01 — SomNambul
    Authors: Gene Abrams, Mark Tomforde
    Subjects: Operator Algebras
    Abstract

    For any countable graph $E$, we investigate the relationship between the
    Leavitt path algebra $L_{\C}(E)$ and the graph C*-algebra $C^*(E)$. For graphs
    $E$ and $F$, we examine ring homomorphisms, ring *-homomorphisms, algebra
    homomorphisms, and algebra *-homomorphisms between $L_{\C}(E)$ and $L_{\C}(F)$.
    We prove that in certain situations isomorphisms between $L_{\C}(E)$ and
    $L_{\C}(F)$ yield *-isomorphisms between the corresponding C*-algebras $C^*(E)$
    and $C^*(F)$.

  2. On the simplicity of Lie algebras associated to Leavitt algebras.

    Втр, 08/18/2009 - 11:53 — SomNambul
    Authors: Gene Abrams, Darren Funk-Neubauer
    Subjects: Rings and Algebras
    Abstract

    For any field $K$ and integer $n\geq 2$ we consider the Leavitt algebra $L =
    L_K(n)$. $L$ is an associative algebra, but we view $L$ as a Lie algebra using
    the bracket $[a,b]=ab-ba$ for $a,b \in L$. We denote this Lie algebra as $L^-$,
    and consider its Lie subalgebra $[L^-,L^-]$. In our main result, we show that
    $[L^-,L^-]$ is a simple Lie algebra if and only if char$(K)$ divides $n-1$. For
    any positive integer $d$ we let $S = M_d(L_K(n))$ be the $d\times d$ matrix
    algebra over $L_K(n)$. We give sufficient conditions for the simplicity and
    non-simplicity of the Lie algebra $[S^-,S^-]$.

Math-arch

RSS-материал