Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nuclearity of semigroup C*-algebras   We study the semigroup C*-algebra of a positive cone P of a weakly
quasi-lattice ordered group. That is, P is a subsemigroup of a discrete group G
with P\cap P^{-1}=\{e\} and such that any two elements of P with a common upper
bound in P also have a least upper bound. We find sufficient conditions for the
semigroup C*-algebra of P to be nuclear. These conditions involve the idea of a
generalised length function, called a "controlled map", into an amenable group.
Here we give a new definition of a controlled map and discuss examples from
different sources. We apply our main result to establish nuclearity for
semigroup C*-algebras of a class of one-relator semigroups, motivated by a
recent work of Li, Omland and Spielberg. This includes all the
Baumslag--Solitar semigroups. We also analyse semidirect products of weakly
quasi-lattice ordered groups and use our theorem in examples to prove
nuclearity of the semigroup C*-algebra. Moreover, we prove that the graph
product of weak quasi-lattices is again a weak quasi-lattice, and show that the
corresponding semigroup C*-algebra is nuclear when the underlying groups are
amenable.

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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas