Freudenthal algebra
In algebra, Freudenthal algebras are certain Jordan algebras constructed from composition algebras.
Definition
Suppose that C is a composition algebra over a field F and a is a diagonal matrix in GLn(F). A reduced Freudenthal algebra is defined to be a Jordan algebra equal to the set of 3 by 3 matrices X over C such that {{overline|X}}Ta=aX. A Freudenthal algebra is any twisted form of a reduced Freudental algebra.
References
- {{citation|mr=0797151 |last=Freudenthal|first= Hans |authorlink=Hans Freudenthal |title=Oktaven, Ausnahmegruppen und Oktavengeometrie|journal= Geom. Dedicata |volume=19 |year=1985|issue= 1|pages= 7–63|origyear=1951|doi=10.1007/BF00233101|s2cid=121496094}}
- {{citation | last1=Knus | first1=Max-Albert | last2=Merkurjev | first2=Alexander | author2-link=Alexander Merkurjev | last3=Rost | first3=Markus | author3-link=Markus Rost | last4=Tignol | first4=Jean-Pierre | title=The book of involutions | zbl=0955.16001 | series=Colloquium Publications | publisher=American Mathematical Society | volume=44 | location=Providence, RI | year=1998 | isbn=0-8218-0904-0 }}
Category:Non-associative algebras
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