4,725 research outputs found
Profinite Groups Associated to Sofic Shifts are Free
We show that the maximal subgroup of the free profinite semigroup associated
by Almeida to an irreducible sofic shift is a free profinite group,
generalizing an earlier result of the second author for the case of the full
shift (whose corresponding maximal subgroup is the maximal subgroup of the
minimal ideal). A corresponding result is proved for certain relatively free
profinite semigroups. We also establish some other analogies between the kernel
of the free profinite semigroup and the \J-class associated to an irreducible
sofic shift
Cuntz-Li relations, Inverse semigroups and Groupoids
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.Comment: Section 8 has undergone substantial revisions. More proofs adde
Semigroup Closures of Finite Rank Symmetric Inverse Semigroups
We introduce the notion of semigroup with a tight ideal series and
investigate their closures in semitopological semigroups, particularly inverse
semigroups with continuous inversion. As a corollary we show that the symmetric
inverse semigroup of finite transformations of the rank
is algebraically closed in the class of (semi)topological inverse
semigroups with continuous inversion. We also derive related results about the
nonexistence of (partial) compactifications of classes of semigroups that we
consider.Comment: With the participation of the new coauthor - Jimmie Lawson - the
manuscript has been substantially revised and expanded. Accordingly, we have
also changed the manuscript titl
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