Albert algebra

In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of non-associative algebras, usually working over the real numbers. Over the real numbers, there is only one such Jordan algebra up to isomorphism. This algebra may be viewed as the set of 3×3 self-adjoint matrices over the octonions with binary operation

:$x\; star\; y\; =\; frac12\; (x\; cdot\; y\; +\; y\; cdot\; x),$

where $cdot$ denotes matrix multiplication.

References

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