Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semicrossed products of C*-algebras and their C*-envelopes   Let $\mathcal{C}$ be a C*-algebra and $\alpha:\mathcal{C} \rightarrow
\mathcal{C}$ a unital *-endomorphism. There is a natural way to construct
operator algebras which are called semicrossed products, using a convolution
induced by the action of $\alpha$ on $\mathcal{C}$. We show that the
C*-envelope of a semicrossed product is (a full corner of) a crossed product.
As a consequence, we get that, when $\alpha$ is *-injective, the semicrossed
products are completely isometrically isomorphic and share the same
C*-envelope, the crossed product $\mathcal{C}_\infty \rtimes_{\alpha_\infty}
\mathbb{Z}$. We show that minimality of the dynamical system
$(\mathcal{C},\alpha)$ is equivalent to non-existence of non-trivial Fourier
invariant ideals in the C*-envelope. We get sharper results for commutative
dynamical systems.

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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: physics