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The C$^*$-envelope of a semicrossed product and nest representations

Justin R. Peters
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Abstract

Let $X$ be compact Hausdorff, and $ϕ: X \to X$ a continuous surjection. Let $\mathcal{A}$ be the semicrossed product algebra corresponding to the relation $fU = Uf\circ ϕ$. Then the C$^*$-envelope of $\mathcal{A}$ is the crossed product of a commutative C$^*$-algebra which contains $C(X)$ as a subalgebra, with respect to a homeomorphism which we construct. We also show there are``sufficiently many'' nest representations.

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Justin R. Peters. 2006-09-19. The C$^*$-envelope of a semicrossed product and nest representations. https://arxiv.org/abs/math/0609533

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