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1954•Canadian Journal of MathematicsOpen access

On Homomorphic Images of Special Jordan Algebras

P. M. Cohn

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Abstract

A linear algebra is called a Jordan algebra if it satisfies the identities (1) ab = ba, (a2b) a = a2(ba). It is well known that a linear algebra S over a field of characteristic different from two is a Jordan algebra if there is an isomorphism a → a of the vector-space underlying S into the vector-space of some associative algebra A such that 1 , where the dot denotes the multiplication in A. Such an algebra S is called a special Jordan algebra.

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A linear algebra is called a Jordan algebra if it satisfies the identities (1) ab = ba, (a2b) a = a2(ba). It is well known that a linear algebra S over a field of characteristic different from two is a Jordan algebra if there is an isomorphism a → a of the vector-space underlying S into the vector-space of some associative algebra A such that 1 , where the dot denotes the multiplication in A. Such an algebra S is called a special Jordan algebra.

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Available abstract

A linear algebra is called a Jordan algebra if it satisfies the identities (1) ab = ba, (a2b) a = a2(ba). It is well known that a linear algebra S over a field of characteristic different from two is a Jordan algebra if there is an isomorphism a → a of the vector-space underlying S into the vector-space of some associative algebra A such that 1 , where the dot denotes the multiplication in A. Such an algebra S is called a special Jordan algebra.

Key concepts: Mathematics, Jordan algebra, Division algebra, Cellular algebra, Algebra over a field, Symmetric algebra, Filtered algebra, Algebra representation

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