弱单调\(C^*\) -代数作为Exel-Laca代数

IF 1 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2024-10-29 DOI:10.1007/s10231-024-01519-y

Vitonofrio Crismale, Simone Del Vecchio, Stefano Rossi, Janusz Wysoczański

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引用次数: 0

摘要

用合适的Exel-Laca代数的商给出了弱单调\(C^*\) -代数的一个抽象表征，即由作用于所谓弱单调Fock空间的创造者和湮灭者所产生的具体\(C^*\) -代数。证明了以\({\mathbb N}\)为索引的弱单调\(C^*\) -代数是I型\(C^*\) -代数，并完全确定了它的表示理论，而以\({\mathbb Z}\)为索引的弱单调\(C^*\) -代数不是I型。

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Weakly-monotone \(C^*\)-algebras as Exel–Laca algebras

An abstract characterization of weakly monotone \(C^*\)-algebras, namely the concrete \(C^*\)-algebras generated by creators and annihilators acting on the so-called weakly monotone Fock spaces, is given in terms of (quotients of) suitable Exel–Laca algebras. The weakly monotone \(C^*\)-algebra indexed by \({\mathbb N}\) is shown to be a type-I \(C^*\)-algebra and its representation theory is entirely determined, whereas the weakly monotone \(C^*\)-algebra indexed by \({\mathbb Z}\) is shown not to be of type I.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.