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Okubo Algebras with Isotropic Norm

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Non-Associative Algebras and Related Topics (NAART 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 427))

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Abstract

Okubo algebras form an important class of nonunital composition algebras of dimension 8. Contrary to what happens for unital composition algebras, they are not determined by their multiplicative norms. Okubo algebras with isotropic norm are characterized here by the existence of a special grading. In the split case, and under some restrictions on the ground field, the automorphism group of the most symmetric of these gradings is the projective unitary group \(\textrm{PU}(3,2^2)\), whose structure is showcased by the grading.

Supported by grant MTM2017-83506-C2-1-P (AEI/FEDER, UE), by grant PID2021-123461NB-C21, funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, and by grants E22_17R and E22_20R (Gobierno de Aragón, Grupo de investigación “Álgebra y Geometría”).

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Authors and Affiliations

  1. Departamento de Matemáticas e Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009, Zaragoza, Spain

    Alberto Elduque

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  1. Alberto Elduque
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Correspondence to Alberto Elduque .

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Editors and Affiliations

  1. Mathematics, University of Coimbra, Coimbra, Portugal

    Helena Albuquerque

  2. Department of Mathematics, Centre for Mathematics of the University of Coimbra, Coimbra, Portugal

    Jose Brox

  3. Mathematics, University of Oviedo, Oviedo, Spain

    Consuelo Martínez

  4. CMUC-Centre for Mathematics of the University of Coimbra, CeBER-Centre for Business and Economics Research, Faculty of Economics, University of Coimbra, Coimbra, Portugal

    Paulo Saraiva

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Elduque, A. (2023). Okubo Algebras with Isotropic Norm. In: Albuquerque, H., Brox, J., Martínez, C., Saraiva, P. (eds) Non-Associative Algebras and Related Topics. NAART 2020. Springer Proceedings in Mathematics & Statistics, vol 427. Springer, Cham. https://doi.org/10.1007/978-3-031-32707-0_18

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