Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonself-adjoint semicrossed products by abelian semigroups   Let $\mathcal{S}$ be the semigroup $\mathcal{S}=\sum^{\oplus
k}_{i=1}\Sc{S}_i$, where for each $i\in I$, $\mathcal{S}_i$ is a countable
subsemigroup of the additive semigroup $\B{R}_+$ containing 0. We consider
representations of $\mathcal{S}$ as contractions $\{T_s\}_{s\in\mathcal{S}}$ on
a Hilbert space with the Nica-covariance property: $T_s^*T_t=T_tT_s^*$ whenever
$t\wedge s=0$. We show that all such representations have a unique minimal
isometric Nica-covariant dilation.
  This result is used to help analyse the nonself-adjoint semicrossed product
algebras formed from Nica-covariant representations of the action of
$\mathcal{S}$ on an operator algebra $\mathcal{A}$ by completely contractive
endomorphisms. We conclude by calculating the $C^*$-envelope of the isometric
nonself-adjoint semicrossed product algebra (in the sense of Kakariadis and
Katsoulis).

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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex