MAXIMALITY OF THE ANALYTIC SUBALGEBRAS OF C*-ALGEBRAS WITH FLOWS

Title & Authors
MAXIMALITY OF THE ANALYTIC SUBALGEBRAS OF C*-ALGEBRAS WITH FLOWS
Kishimoto, Akitaka;

Abstract
Given a faithful flow $\small{{\alpha}}$ on a $\small{C^*}$-algebra A, when A is $\small{{\alpha}}$-simple we will show that the closed subalgebra of A consisting of elements with non-negative Arveson spectra is maximal if and only if the crossed product of A by $\small{{\alpha}}$ is simple. We will also show how the general case can be reduced to the $\small{{\alpha}}$-simple case, which roughly says that any flow with the above maximality is an extension of a trivial flow by a flow of the above type in the $\small{{\alpha}}$-simple case. We also propose a condition of essential maximality for such closed subalgebras.
Keywords
Arveson spectrum;maximal subalgebra;crossed product;
Language
English
Cited by
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