Endomorphisms and Modular Theory of 2-Graph C*-Algebras
Endomorphisms and Modular Theory of 2-Graph C*-Algebras
复制标题
2-图C*-代数的自同态和模理论
DOI：
10.1512/iumj.2010.59.3973
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Dilian Yang
中科院分区：
文献类型：
--
作者：
Dilian Yang
本文研究了单顶点上2-图的C*-代数的自同态和模理论。证明了具有扭曲性质的么正自同态与其酉偶之间存在半群同构.刻划了自同态保持规范自同构的不动点代数Ff$及其典范MASA$\Fd$的条件。还研究了自同态的一些其他性质。
就模理论而言，我们证明了模Hilbert代数是由模的生成元生成的代数*-代数。由此，我们得到了由$omega$的GNS表示生成的von Neumann代数$pi(Otheta)“$是第III型$1$的AFD因子，其中$m，n$分别是次数为$(1，0)$和$(0，1)$的生成元的个数.
这项工作是Davidson-Power-Yang和Davidson-Yang的Cite{DPY1，DPY2}的继续。
In this paper, we initiate the study of endomorphisms and modular theory of the graph C*-algebras $\O_{\theta}$of a 2-graph $\Fth$ on a single vertex. We prove that there is a semigroup isomorphism between unital endomorphisms of $\O_{\theta}$ and its unitary pairs with a \textit{twisted property}. We characterize when endomorphisms preserve the fixed point algebra $\fF$ of the gauge automorphisms and its canonical masa $\fD$. Some other properties of endomorphisms are also investigated.
As far as the modular theory of $\O_{\theta}$ is concerned, we show that the algebraic *-algebra generated by the generators of $\O_{\theta}$ with the inner product induced from a distinguished state $\omega$ is a modular Hilbert algebra. Consequently, we obtain that the von Neumann algebra $\pi(\O_{\theta})"$ generated by the GNS representation of $\omega$ is an AFD factor of type III$_1$, provided $\frac{\ln m}{\ln n}\not\in\bQ$. Here $m,n$ are the numbers of generators of $\Fth$ of degree $(1,0)$ and $(0,1)$, respectively.
This work is a continuation of \cite{DPY1, DPY2} by Davidson-Power-Yang and \cite{DY} by Davidson-Yang.
影响因子：
1.7
作者：
Power S
通讯作者：
Power S