The inner structure of boundary quotients of right LCM semigroups

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. 1627-1661. 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 p-adic 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:

0022-2518

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

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