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Semigroup theory of symmetry

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Abstract

Symmetry is one of the most fundamental concepts of all nature. We discuss the general theory of symmetry based on theory of semigroups. This includes and extends the theory of groups, which is by now broadly used as an algebraic tool for studying many types of symmetries observed by people. However, symmetry groups are only a particular case of more general, symmetry semigroups. The latter are in turn an instance of an even more general groupoids of symmetry, which may further be a topic of special consideration.

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Acknowledgments

We are grateful to the Department of Mathematics, UCD, for providing an office so that Dr. Nordahl may more directly participate in mathematical activity now that he is Professor Emeritus of the Department of Psychiatry and Behavioral Sciences. We are also grateful to our anonymous Referees for all their suggestions. The support of the Ministry of Absorption of the State Israel (through fellowship “Shapiro”) is acknowledged.

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Authors and Affiliations

  1. Department of Computer Science and Mathematics, Ariel University, 40700, Ariel, Israel

    Vladimir R. Rosenfeld

  2. Department of Psychiatry and Behavioral Sciences, University of California Davis, Davis, CA, 95616, USA

    Thomas E. Nordahl

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  1. Vladimir R. Rosenfeld
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  2. Thomas E. Nordahl
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Correspondence to Vladimir R. Rosenfeld.

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Rosenfeld, V.R., Nordahl, T.E. Semigroup theory of symmetry. J Math Chem 54, 1758–1776 (2016). https://doi.org/10.1007/s10910-016-0653-4

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