The set of derivations on these mathematical objects is a semisimple Lie algebra of dimension 14; Élie Cartan showed that their automorphism group is the smallest of the exceptional Lie groups.
The set of derivations on these mathematical objects is a semisimple Lie algebra of dimension 14; Élie Cartan showed that their automorphism group is the smallest of the exceptional Lie groups. The nonzero members of this alternative algebra form a nonassociative Moufang loop under their namesake multiplication. This number system is the largest normed division algebra; the Fano plane can be used to multiply the units in it. The projective plane over this number system is named for(*) Cayley; one method of constructing them is named for Cayley and Dickson. In this non-associative number system, multiplying any non-identity element of this number system by itself gives the negative of the identity element. The discoverer of this number system was inspired by William Hamilton and used it to express the product of two sums of eight squares as another sum of eight squares. For 10 points, name this system invented by John Graves, an extension of the quaternions.
The set of derivations on these mathematical objects is a semisimple Lie algebra of dimension 14; Élie Cartan showed that their automorphism group is the smallest of the exceptional Lie groups.
octonions [prompt on "octaves"]