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A 2-dimensional quaternionic construction of an 8-dimensional ternary composition algebra

Двумерная кватернионная конструкция для восьмимерной алгебры трехкомцонентных соединений

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Il Nuovo Cimento B (1971-1996)

Summary

It is shown that a real 8-dimensional ternary composition algebra can be constructed out of a quaternionic 2-dimensional Hilbert space. The construction is seen to highlight a subgroup Spin(5)Pin(2) of the automorphism group Spin(7) of the algebra.

Riassunto

Si mostra che un’algebra reale a composizione ternaria otto-dimensionale può essere costruita da uno spazio di Hilbert a due dimensioni quaternionico. Si vede che la costruzione mette in evidenza un subgruppo Spin(5) Pin(2) del gruppo di automorfismo Spin(7) dell’algebra.

Резюме

Показывается, что вещественная восъмимерная алгебра трехкомпонентных соединений может быть сконструирована в кватернионном двумерном Гильбертовом пространстве. Эта конструкция придает большое значение подгруппе Spin(5) Pin(2) для группы автоморфизма Spin(7) этой алгебры.

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Authors and Affiliations

  1. School of Mathematics, University of Hull, HU6 7RX, Hull, UK

    R. Shaw

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  1. R. Shaw
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Shaw, R. A 2-dimensional quaternionic construction of an 8-dimensional ternary composition algebra. Nuov Cim B 104, 163–176 (1989). https://doi.org/10.1007/BF02906314

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  • DOI: https://doi.org/10.1007/BF02906314

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