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About Nonassociativity in Mathematics and Physics

Acta Applicandae Mathematica volume 50, pages 3–31 (1998)Cite this article

Abstract

A short review about nonassociative algebraic systems (mainly nonassociative algebras) and their physical applications is presented. We begin with some motivations, then we give a brief historical overview about the formation and development of the concept of hypercomplex number system and about some earlier applications. The main directions discussed are the octonionic, Lie-admissible, and quasigroup approaches. Also, some problems investigated in Tartu, the octonionic approach, Moufang–Mal'tsev symmetry, and associator quantization are discussed. This review does not pretend to be complete as the accent is placed on ideas and not on the techniques, also the references are quite sporadic (there are many authors and results mentioned in the text without references).

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Authors and Affiliations

  1. Institute of Physics, Estonian Academy of Sciences, Riia 142, EE2400, Tartu, Estonia

    Jaak Lõhmus

  2. Department of Mathematics, Tallinn Technical University, Akadeemia tee 1, EE0108, Tallinn, Estonia

    Eugen Paal

  3. Institute of Astrophysics and Atmospheric Physics, Estonian Academy of Sciences, Tõravere Observatory, EE2444 District of Tartu, Estonia

    Leo Sorgsepp

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  1. Jaak Lõhmus
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Lõhmus, J., Paal, E. & Sorgsepp, L. About Nonassociativity in Mathematics and Physics. Acta Applicandae Mathematicae 50, 3–31 (1998). https://doi.org/10.1023/A:1005854831381

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