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

Given a faithful flow ${\alpha}$ on a $C^*$-algebra A, when A is ${\alpha}$-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 ${\alpha}$ is simple. We will also show how the general case can be reduced to the ${\alpha}$-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 ${\alpha}$-simple case. We also propose a condition of essential maximality for such closed subalgebras.