IUMJ

Title: $C^*$-envelopes of universal free products and semicrossed products for multivariable dynamics

Authors: Benton L. Duncan

Issue: Volume 57 (2008), Issue 4, 1781-1788

Abstract:

We show that, for a class of operator algebras satisfying a natural condition, the $C^{*}$-envelope of the universal free product of operator algebras $A_i$ is given by the free product of the $C^{*}$-envelopes of the $A_i$. We apply this theorem to, in special cases, the $C^{*}$-envelope of the semicrossed products for multivariable dynamics in terms of the single variable semicrossed products of Peters.