uniqueness — 2 articles found.

A New Uniqueness Theorem for the Tight C*-algebra of an Inverse Semigroup

C. R. Math. Rep. Acad. Sci. Canada Vol. 44 (4) 2022, pp. 88–112
Vol.44 (4) 2022
Charles Starling Details
(Received: 2022-11-30 )
(Received: 2022-11-30 )

Charles Starling, Carleton University, School of Mathematics and Statistics. 4302 Herzberg Laboratories, Ottawa ON, K1S 5B6; e-mail: cstar@math.carleton.ca


We prove a new uniqueness theorem for the tight C*-algebras of an inverse semigroup by generalising the uniqueness theorem given for étale groupoid C*-algebras by Brown, Nagy, Reznikoff, Sims, and Williams. We use this to show that in the nuclear and Hausdorff case, a *-homomorphism from the boundary quotient C*-algebra of a right LCM monoid is injective if and only if it is injective on the subalgebra generated by the core submonoid. We also use our result to clarify the identity of the tight C*-algebra of an inverse semigroup we previously associated to a subshift and erroneously identified as the Carlsen-Matsumoto algebra.

Nous prouvons un nouveau thèoréme d’unicité pour les C*-algèbres serrées d’un semi-groupe inverse en généralisant le théorème d’unicité donné pour les C*-algèbres groupoides étales par Brown, Nagy, Reznikoff, Sims et Williams. Nous utilisons ceci pour montrer que dans le cas nucléaire et de Hausdorff, un *-homomorphisme de l’algèbre C* du quotient aux limites d’un monoïde LCM droit est injectif si et seulement s’il est injectif sur la sous-algèbre générée par le sous-monoide de noyau. Nous utilisons également notre résultat pour clarifier l’identité de l’algèbre C* serrée d’un semi-groupe inverse que nous avons précédemment associé à un sous-décalage et identifié à tort comme l’algèbre de Carlsen-Matsumoto.

Keywords: C*-algebra, LCM semigroup, groupoid, inverse semigroup, subshift, tight representation, uniqueness

AMS Subject Classification: Groupoids; semigroupoids; semigroups; groups (viewed as categories), Inverse semigroups, General theory of $C^*$-algebras 18B40, 20M18, 46L05

PDF(click to download): A New Uniqueness Theorem for the Tight C*-algebra of an Inverse Semigroup

A remark on inhomogeneous Cauchy problems

C. R. Math. Rep. Acad. Sci. Canada Vol. 23 (1) 2001, pp. 22–27
Vol.23 (1) 2001
S. Amat / S. Busquier Details
(Received: 2000-08-07 )
(Received: 2000-08-07 )

S. Amat / S. Busquier


No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: existence, inhomogeneous Cauchy problems, uniqueness

AMS Subject Classification: Initial value problems for nonlinear first-order PDE; nonlinear evolution equations, Initial value problems for nonlinear higher-order PDE; nonlinear evolution equations, , 35F25, 35G25, 3SF10, 47D05

PDF(click to download): A remark on inhomogeneous Cauchy problems

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