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Cartan subalgebras for non-principal twisted groupoid C⁎-algebras
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.jfa.2020.108611
A. Duwenig , E. Gillaspy , R. Norton , S. Reznikoff , S. Wright

Abstract Renault proved in 2008 [22, Theorem 5.2] that if G is a topologically principal groupoid, then C 0 ( G ( 0 ) ) is a Cartan subalgebra in C r ⁎ ( G , Σ ) for any twist Σ over G . However, there are many groupoids which are not topologically principal, yet their (twisted) C ⁎ -algebras admit Cartan subalgebras. This paper gives a dynamical description of a class of such Cartan subalgebras, by identifying conditions on a 2-cocycle c on G and a subgroupoid S ⊆ G under which C r ⁎ ( S , c ) is Cartan in C r ⁎ ( G , c ) . When G is a discrete group, we also describe the Weyl groupoid and twist associated to these Cartan pairs, under mild additional hypotheses.

中文翻译:

非主扭曲群群 C⁎-代数的嘉当子代数

摘要 Renault 在 2008 年证明了 [22, Theorem 5.2] 如果 G 是拓扑主群群,则 C 0 ( G ( 0 ) ) 是 C r ⁎ ( G , Σ ) 中的 Cartan 子代数,对于 G 上的任何扭曲 Σ。然而,有许多群群不是拓扑主体,但它们的(扭曲的)C ⁎ -代数承认嘉当子代数。本文通过确定 G 上的 2-cocycle c 和子群 S ⊆ G 上的条件,其中 C r ⁎ ( S , c ) 是 C r ⁎ ( G , C ) 。当 G 是一个离散群时,我们还描述了与这些 Cartan 对相关的 Weyl groupoid 和扭曲,在温和的附加假设下。
更新日期:2020-10-01
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