Difference between revisions of "Albert algebra"

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The operation is commutative but not associative.  It is an example of an exceptional [[Jordan algebra]].  Because most other exceptional Jordan algebras are constructed using this one, it is often referred to as "the" exceptional Jordan algebra.
The operation is commutative but not associative.  It is an example of an exceptional [[Jordan algebra]].  Because most other exceptional Jordan algebras are constructed using this one, it is often referred to as "the" exceptional Jordan algebra.


[[Category:Nonassociative algebras]]
==References==
* A V Mikhalev, Gunter F Pilz, "The Concise Handbook of Algebra", Springer, 2002, ISBN 0792370724, page 346.

Revision as of 15:01, 26 October 2008

The Albert algebra is the set of 3×3 self-adjoint matrices over the octonions with binary operation

where denotes matrix multiplication.

The operation is commutative but not associative. It is an example of an exceptional Jordan algebra. Because most other exceptional Jordan algebras are constructed using this one, it is often referred to as "the" exceptional Jordan algebra.

References

  • A V Mikhalev, Gunter F Pilz, "The Concise Handbook of Algebra", Springer, 2002, ISBN 0792370724, page 346.