Abstract
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∈S. These algebras contain a four-dimensional subalgebra which can be viewed as a generalization of a (nonassociative) quaternion algebra. The four-dimensional algebras are studied independently.Over R, this construction can be used to generate 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 as well.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
