Some remarks on the transformation groupoid C*-algebras

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• afrae Afrae tanzite (None / Other)
• Thursday 03 July 2025, 11:45-11:50
• External.

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TGAW01 - Crossed products and groupoid C*-algebras

Let $G$ be a discrete group acting on a Hausdorff compact space $X$ and $U$ be the unitary group of $C(X)$, the algebra of continuous functions on $X$. In this paper we show that there exists a *-homomorpism that connect every groupoid algebra associated with the \’etale transformation groupoid $X \times G$ to the group algebra associated to the semi direct product $ U \rtimes G$. As consequences, the groupoid Banach algebra $\ell^{(X \times G)$ is amenable if the acting group $G$ is amenable. In the other hand, if $ G $ is finite then $\ell}{I}(X \times G)$ is hermitian.

This talk is part of the Isaac Newton Institute Seminar Series series.

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