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Commutants in crossed product algebras for piecewise constant functions on the real line
Makerere University, UGA.
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.ORCID iD: 0000-0003-3931-7358
Mälardalens Högskola, SWE.
2020 (English)In: Springer Proceedings in Mathematics and Statistics / [ed] Silvestrov S.,Malyarenko A.,Rancic M., Springer , 2020, Vol. 317, p. 427-444Conference paper, Published paper (Refereed)
##### Abstract [en]

In this paper we consider commutants in crossed product algebras, for algebras of piece-wise constant functions on the real line acted on by the group of integers Z. The algebra of piece-wise constant functions does not separate points of the real line, and interplay of the action with separation properties of the points or subsets of the real line by the function algebra become essential for many properties of the crossed product algebras and their subalgebras. In this article, we deepen investigation of properties of this class of crossed product algebras and interplay with dynamics of the actions. We describe the commutants and changes in the commutants in the crossed products for the canonical generating commutative function subalgebras of the algebra of piece-wise constant functions with common jump points when arbitrary number of jump points are added or removed in general positions, that is when corresponding constant value set partitions of the real line change, and we give complete characterization of the set difference between commutants for the increasing sequence of subalgebras in crossed product algebras for algebras of functions that are constant on sets of a partition when partition is refined. © Springer Nature Switzerland AG 2020.

##### Place, publisher, year, edition, pages
Springer , 2020. Vol. 317, p. 427-444
##### Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1017, E-ISSN 2194-1009
##### Keywords [en]
Commutant, Crossed product algebra, Partition, Piece-wise constant functions, Random processes, Stochastic systems, Arbitrary number, Commutative functions, Constant values, Crossed product algebras, Function algebra, Piece-wise-constant functions, Separation Property, Set partitions, Algebra
##### National Category
Algebra and Logic
##### Identifiers
Scopus ID: 2-s2.0-85087533269ISBN: 9783030418496 (print)OAI: oai:DiVA.org:bth-20254DiVA, id: diva2:1457085
##### Conference
International Conference on Stochastic Processes and Algebraic Structures, SPAS 2017, Västerås and Stockholm, Sweden, 4 October 2017 through 6 October 2017
##### Funder
Sida - Swedish International Development Cooperation Agency
##### Note

Open access

Available from: 2020-08-10 Created: 2020-08-10 Last updated: 2023-03-24Bibliographically approved

#### Open Access in DiVA

No full text in DiVA

Publisher's full textScopus

Richter, Johan

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##### By organisation
Department of Mathematics and Natural Sciences
##### On the subject
Algebra and Logic

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Cite
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