Definition:Cayley Algebra

Definition

The Cayley algebra is the non-associative division algebra formed by the octonions under octonion multiplication.

Also see

• Octonions form Algebra

Source of Name

This entry was named for Arthur Cayley.

Historical Note

The octonions were first discovered by John Thomas Graves in $1843$.

However, Arthur Cayley in $1845$ was the to discuss the Cayley algebra in print.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Cayley algebra
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.26$: Extensions of the Complex Number System. Algebras, Quaternions, and Lagrange's Four Squares Theorem
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cayley algebra (J.T. Graves, 1843)