| Popis: |
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. |
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