Aiello, Valeriano; Conti, Roberto; Rossi, Stefano; Stammeier, Nicolai (2020). The inner structure of boundary quotients of right LCM semigroups. Indiana University mathematics journal, 69(5), pp. 16271661. Dept. of Mathematics, Indiana University 10.1512/iumj.2020.69.8006

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We study distinguished subalgebras and automorphisms of boundary quotients arising from algebraic dynamical systems (G, P, θ). Our work includes a complete solution to the problem of extending Bogolubov automorphisms from the Cuntz algebra in 2 ≤ p < ∞ generators to the padic ring C^*algebra. For the case where P is abelian and C^*(G) is a maximal abelian subalgebra, we establish a picture for the automorphisms of the boundary quotient that fix C^*(G) pointwise. This allows us to show that they form a maximal abelian subgroup of the entire automorphism group. The picture also leads to the surprising outcome that, for integral dynamics, every automorphism that fixes one of the natural Cuntz subalgebras pointwise is necessarily a gauge automorphism. Many of the automorphisms we consider are shown to be outer.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics 
UniBE Contributor: 
Aiello, Valeriano 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
00222518 
Publisher: 
Dept. of Mathematics, Indiana University 
Funders: 
[UNSPECIFIED] Research Council of Norway 
Language: 
English 
Submitter: 
Sebastiano Don 
Date Deposited: 
09 Feb 2021 14:05 
Last Modified: 
09 Feb 2021 14:05 
Publisher DOI: 
10.1512/iumj.2020.69.8006 
ArXiv ID: 
1709.08839 
BORIS DOI: 
10.48350/151253 
URI: 
https://boris.unibe.ch/id/eprint/151253 