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- Title
A Generalization of the First Tits Construction.
- Authors
Moran, Thomas; Pumpluen, Susanne
- Abstract
Let F be a field of characteristic, not 2 or 3. The first Tits construction is a well-known tripling process to construct separable cubic Jordan algebras, especially Albert algebras. We generalize the first Tits construction by choosing the scalar employed in the tripling process outside of the base field. This yields a new family of non-associative unital algebras which carry a cubic map, and maps that can be viewed as generalized adjoint and generalized trace maps. These maps display properties often similar to the ones in the classical setup. In particular, the cubic norm map permits some kind of weak Jordan composition law.
- Subjects
JORDAN; NONASSOCIATIVE algebras; GENERALIZATION; JORDAN algebras
- Publication
Axioms (2075-1680), 2024, Vol 13, Issue 5, p299
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms13050299