Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular Dilation on Graph Products of $\mathbb{N}$   We extended the definition of regular dilation to graph products of
$\mathbb{N}$, which is an important class of quasi-lattice ordered semigroups.
Two important results in dilation theory are unified under our result: namely,
Brehmer's regular dilation on $\mathbb{N}^k$ and Frazho-Bunce-Popescu's
dilation of row contractions. We further show that a representation of a graph
product has an isometric Nica-covariant dilation if and only if it is
$\ast$-regular. A special case of our result was considered by Popescu, and we
studied the connection with Popescu's work.

31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn