Albert algebra: Difference between revisions
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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 | ||
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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: | ==References== | ||
* A V Mikhalev, Gunter F Pilz, "The Concise Handbook of Algebra", Springer, 2002, ISBN 0792370724, page 346.[[Category:Suggestion Bot Tag]] | |||
Latest revision as of 07:00, 8 July 2024
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.