TL;DR
This survey paper reviews the theory, classification, and applications of composition algebras, including quaternions, octonions, and symmetric composition algebras, highlighting their algebraic properties and triality phenomena.
Contribution
It provides a comprehensive overview of composition algebras, their classifications, and their role in algebraic triality, consolidating existing knowledge and applications.
Findings
Classical algebras of quaternions and octonions are reviewed.
Main properties and classifications of unital and symmetric composition algebras are summarized.
Algebraic triality using symmetric composition algebras is discussed.
Abstract
This paper is devoted to survey composition algebras and some of their applications. After overviewing the classical algebras of quaternions and octonions, both unital composition algebras (or Hurwitz algebras) and symmetric composition algebras will be dealt with. Their main properties, as well as their classifications, will be reviewed. Algebraic triality, through the use of symmetric composition algebras, will be considered too.
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