# 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

- Mathematics
- Proceedings of the American Mathematical Society
- 2019

The loop algebra construction by Allison, Berman, Faulkner, and Pianzola, describes graded-central-simple algebras with split centroid in terms of central simple algebras graded by a quotient of the… Expand

Graded-division algebras and Galois extensions

- Mathematics
- 2020

Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms… Expand

Graded-division algebras over arbitrary fields

- Mathematics
- 2019

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading… Expand

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