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arXiv · 1807.00057

On nonassociative graded-simple algebras over the field of real numbers

Yuri Bahturin·Mikhail Kochetov
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Abstract

We extend the loop algebra construction for algebras graded by abelian groups to study graded-simple algebras over the field of real numbers (or any real closed field). As an application, we classify up to isomorphism the graded-simple alternative (nonassociative) algebras and graded-simple finite-dimensional Jordan algebras of degree 2. We also classify the graded-division alternative (nonassociative) algebras up to equivalence.

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Yuri Bahturin, Mikhail Kochetov. 2018-06-29. On nonassociative graded-simple algebras over the field of real numbers. https://arxiv.org/abs/1807.00057

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