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Reordering in Noncommutative Algebras Associated with Iterated Function Systems

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Algebraic Structures and Applications (SPAS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 317))

Abstract

A general class of multi-parametric families of unital associative complex algebras, defined by commutation relations associated with group or semigroup actions of dynamical systems and iterated function systems, is considered. A generalization of these commutation relations in three generators is also considered, modifying Lie algebra type commutation relations, typical for usual differential or difference operators, to relations satisfied by more general twisted difference operators associated with general twisting maps. General reordering and nested commutator formulas for arbitrary elements in these algebras are presented, and some special cases are considered, generalizing some well-known results in mathematics and physics.

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Acknowledgements

This research was supported by the Swedish International Development Cooperation Agency (Sida), International Science Programme (ISP) in Mathematical Sciences (IPMS), Eastern Africa Universities Mathematics Programme (EAUMP). John Musonda is also grateful to the research environment Mathematics and Applied Mathematics (MAM), Division of Applied Mathematics, Mälardalen University and to the Department of Mathematics and Statistics, University of Zambia, for providing an excellent and inspiring environment for research.

We are also grateful to Lars Hellström for fruitful suggestions on Proposition 22.1.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, School of Natural Sciences, The University of Zambia, Box 32371, Lusaka, Zambia

    John Musonda

  2. Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, 37179, Karlskrona, Sweden

    Johan Richter

  3. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Box 883, 72123, Västerås, Sweden

    Sergei Silvestrov

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  1. John Musonda
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Correspondence to John Musonda .

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Editors and Affiliations

  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

  2. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Anatoliy Malyarenko

  3. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Milica Rančić

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Musonda, J., Richter, J., Silvestrov, S. (2020). Reordering in Noncommutative Algebras Associated with Iterated Function Systems. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Algebraic Structures and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-030-41850-2_22

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