Dynamical Systems and Analysis Seminar - Rachid El Harti
| Dates: | 20 April 2026 |
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| Times: | 14:00 - 14:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Rachid El Harti (Hassan University)
Title: Embedding theorems in Groupoid C*-algebras
Abstract: Since groupoids generalize groups, we explore whether the theory of group algebras can be extended to groupoid algebras. We define the convolution algebra C_c(G), the Banach algebra L^1(G), and both the full and the reduced C*-algebras C^*(G) and C^*_r(G) associated with a locally compact groupoid G.
Let G be a discrete group acting on a locally compact Hausdorff space X, and let U denote the unitary group of C_b(X), the C^*-algebra of bounded continuous functions on X. In this paper, we show that the transformation groupoid C^*-algebra C^*(X \times G) is a quotient of the group C^*-algebra C^*(U\rtimes G) associated with the semidirect product U\rtimes G.
Furthermore, we address embedding problems for subgroupoid C*-algebras: given a locally compact groupoid G and an open subgroupoid H\subset G, we prove the existence of injective *-homomorphisms \iota : C^*_r(H) \hookrightarrow C^*_r(G) and similarly for the full C*-algebras. We also show that these embeddings extend naturally to their duals and double duals. This extends the classical embedding theory for groups, where the C*-algebras of an open subgroup embed naturally into those of the ambient group.
Room: Frank Adams 1
Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
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Frank Adams 1
Alan Turing Building
Manchester
