Cuntz-Li relations, Inverse semigroups and Groupoids

Details Cuntz-Li relations, Inverse semigroups and Groupoids Cuntz-Li relations, Inverse semigroups and Groupoids

2012-01-23

arxiv.org/abs/1201.4620v2

Mathematics

Operator Algebras

Section 8 has undergone substantial revisions. More proofs added

Scientific paper

In this paper we show that the universal C*-algebra satisfying the Cuntz-Li
relations is generated by an inverse semigroup of partial isometries. We apply
Exel's theory of tight representations to this inverse semigroup. We identify
the universal C*-algebra as the C*-algebra of the tight groupoid associated to
the inverse semigroup.

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