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Generalized Hurwitz theorem states that there are fifteen composition algebras: seven unital, six para-unital, and two non-unital algebras. In this article we explore the recovery of such algebras from 3D Geometric Algebras. Different involutions, such as reversion, inversion, Clifford conjugation, and full grade inversion, are introduced in order to recover the norm of all composition algebras. A special attention is given to composition algebras of dimension 8, i. e. octonions, paraoctonions and Okubo algebra, for which the introduction of a different product is needed.
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Springer Nature Switzerland
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Sem licença CC