Jordan algebras over algebraic varieties
Susanne Pumpluen
TL;DR
This paper develops a framework for constructing Jordan algebras over algebraic varieties, extending classical methods and providing new examples related to Albert algebras over Brauer-Severi varieties.
Contribution
It generalizes the Tits process to algebraic varieties and constructs new examples of Albert algebras over Brauer-Severi varieties.
Findings
Construction of Jordan algebras over algebraic varieties
General results on algebra structure
Examples of Albert algebras over Brauer-Severi varieties
Abstract
We construct Jordan algebras over a locally ringed space using generalizations of the Tits process and the first Tits construction by Achhammer. Some general results on the structure of these algebras are obtained. Examples of Albert algebras over a Brauer-Severi variety with associated central simple algebra of degree 3 are given.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Advanced Algebra and Geometry