Real non-unital division algebras with su(3) as derivation algebra
We obtain a family of non-unital eight-dimensional division algebras
over a field F out of a separable quadratic field extension S of F, a
three-dimensional anisotropic hermitian form over S of determinant one and
three invertible elements c,d,e in S. The algebras always contain a
four-dimensional subalgebra, which can be viewed as a generalization of a
(nonassociative) quaternion algebra and are studied independently. Over the
reals, this construction can be used to yield division algebras with derivation
algebra isomorphic to su(3) which are the direct sum of two one-dimensional
modules and a six-dimensional irreducible su(3)-module. Albert isotopes with
derivation algebra isomorphic to su(3) are considered briefly.
S. Pumpluen < susanne.pumpluen@nottingham.ac.uk >