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

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

2007-10-16

arxiv.org/abs/0710.3069v1

Indiana University Mathematics Journal 57 (2008), 1781-1788.

Mathematics

Operator Algebras

7 pages

Scientific paper

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.

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