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Commutants in Crossed Product Algebras for Piece-Wise Constant Functions
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-3931-7358
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Makerere University. (MAM)
2016 (English)In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and OptimizationEditors / [ed] Sergei Silvestrov; Milica Rančić, Springer, 2016, p. 95-108Chapter in book (Refereed)
Abstract [en]

In this paper we consider crossed product algebras of algebras of piecewiseconstant functions on the real line with Z. For an increasing sequence of algebras (in which case the commutants form a decreasing sequence), we describe the set difference between the corresponding commutants.

Place, publisher, year, edition, pages
Springer, 2016. p. 95-108
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009 ; 179
Keywords [en]
crossed product algebras, piecewiseconstant functions, commutants
National Category
Mathematics Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-33243DOI: 10.1007/978-3-319-42105-6_7Scopus ID: 2-s2.0-85013026914OAI: oai:DiVA.org:mdh-33243DiVA, id: diva2:974176
Funder
Sida - Swedish International Development Cooperation AgencyAvailable from: 2016-09-25 Created: 2016-09-25 Last updated: 2018-04-17Bibliographically approved
In thesis
1. Dynamical Systems and Commutants in Non-Commutative Algebras
Open this publication in new window or tab >>Dynamical Systems and Commutants in Non-Commutative Algebras
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis work is about commutativity which is a very important topic in Mathematics, Physics, Engineering and many other fields. In Mathematics, it is well known that matrix multiplication (or composition of linear operators on a finite dimensional vector space) is not always commutative. Commuting matrices or more general linear or non-linear operators play an essential role in Mathematics and its applications in Physics and Engineering. Many important relations in Mathematics, Physics and Engineering are represented by operators satisfying a number of commutation relations. Such commutation relations are key in areas such as representation theory, dynamical systems, spectral theory, quantum mechanics, wavelet analysis and many others.

In Chapter 2 of this thesis we treat commutativity of monomials of operators satisfying certain commutation relations in relation to one-dimensional dynamical systems. We derive explicit conditions for commutativity of the said monomials in relation to the existence of periodic points of certain onedimensional dynamical systems.

In Chapter 3, we treat the crossed product algebra for the algebra of piecewise constant functions on given set and describe the commutant of this algebra of functions which happens to be the maximal commutative subalgebra of the crossed product containing this algebra.

In Chapters 4 and 5, we give a characterization of the commutant for the algebra of piecewise constant functions on the real line, by comparing commutants for a non-decreasing sequence of algebras.

In Chapter 6 we give a description of the centralizer of the coefficient algebra in the Ore extension of the algebra of functions on a countable set with finite support.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2018. p. 140
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 258
National Category
Natural Sciences
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-39000 (URN)978-91-7485-381-0 (ISBN)
Public defence
2018-05-29, Kappa, Mälardalens högskola, Västerås, 13:00 (English)
Opponent
Supervisors
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2018-04-17 Created: 2018-04-13 Last updated: 2018-05-07Bibliographically approved

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Richter, Johan

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Citation style
  • apa
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Output format
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