Laca's dilation theorem revisited

Hui Li

*(North China Electric Power University)*

14:00-15:00, July 11, 2024 Science Building A503

__Abstract:__

Let P be a subsemigroup of a group G satisfying G=P^{-1}P, let A=C(X) where X is a compact Hausdorff space, and let \alpha: P \rightarrow End(A) be a semigroup homomorphism such that \alpha_p is unital and injective for all p \in P. Laca's Dilation Theorem asserts that there exists a dynamical system (X_{\infty}, G, \gamma) (X_{\infty} is compact Hausdorff), such that the crossed product of A by P is Morita equivalent to the crossed product of C(X_{\infty}) by G. In this talk, we provide a concrete description of X_{\infty} and \gamma based on Laca's proof. This is joint work with my master student Xiaohui Chen.

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