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

@article{Bahturin2019OnNG,
  title={On nonassociative graded-simple algebras over
 the field of real numbers},
  author={Yuri A. Bahturin and Mikhail Kochetov},
  journal={Tensor Categories and Hopf Algebras},
  year={2019}
}
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. 
4 Citations
Graded-simple algebras and cocycle twisted loop algebras
  • A. Elduque
  • Mathematics
  • Proceedings of the American Mathematical Society
  • 2019
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