论文标题
扭曲的clopoid l^p-operator代数的刚度
Rigidity of twisted groupoid L^p-operator algebras
论文作者
论文摘要
在本文中，我们将研究减少的扭曲组和groupoid $ l^p $ operator代数的同构问题。对于本地紧凑的组$ g $和连续的2个循环$σ$，我们将定义减少的$σ$ twisted $ l^p $ - 操作员algebra $f_λ^p（g，σ）$。我们将证明，如果$ p \ neq2 $，那么两个这样的代数是同构的，并且仅当这些组在拓扑上是同构的，并且连续的2个晶体是共同的。对于twist $ \ MATHCAL {E} $上的étalegroupoid $ \ Mathcal {G} $，我们定义了减少的扭曲的twisted groupoid $ l^p $ - operator algebra $ f^p_λ（\ Mathcal {g}; \ nathcal {e}）$。在本文的主要结果中，我们表明，对于$ p \ neq 2 $，如果topogologids在拓扑上是主要的，Hausdorff，étale，并且具有紧凑的单位空间，则仅在且只有同粒子是同义的，并且当群体素质是同等的，并且Twists是同等的，并且Twists是同等的，并且曲折是同构的，并且曲折是同等的，并且适当地同符。
In this paper we will study the isomorphism problem for the reduced twisted group and groupoid $L^p$-operator algebras. For a locally compact group $G$ and a continuous 2-cocycle $σ$ we will define the reduced $σ$-twisted $L^p$-operator algebra $F_λ^p(G,σ)$. We will show that if $p\neq2$, then two such algebras are isometrically isomorphic if and only if the groups are topologically isomorphic and the continuous 2-cocyles are cohomologous. For a twist $\mathcal{E}$ over an étale groupoid $\mathcal{G}$, we define the reduced twisted groupoid $L^p$-operator algebra $F^p_λ(\mathcal{G};\mathcal{E})$. In the main result of this paper, we show that for $p\neq 2$ if the groupoids are topologically principal, Hausdorff, étale and have a compact unit space, then two such algebras are isometrically isomorphic if and only if the groupoids are isomorphic and the twists are properly isomorphic.
