# Difference between revisions of "Albert algebra"

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The '''Albert algebra''' is the set of 3×3 [[self-adjoint]] matrices over the [[octonion]]s with binary operation | The '''Albert algebra''' is the set of 3×3 [[self-adjoint]] matrices over the [[octonion]]s with binary operation | ||

## Latest revision as of 13:53, 14 November 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.