1. On nonassociative graded-simple algebras over the field of real numbers
- Author
-
Mikhail Kochetov and Yuri Bahturin
- Subjects
Pure mathematics ,Loop algebra ,Mathematics::Commutative Algebra ,Mathematics::Rings and Algebras ,010102 general mathematics ,Field (mathematics) ,Mathematics - Rings and Algebras ,0102 computer and information sciences ,01 natural sciences ,Real closed field ,16W50 (Primary) 17D05, 17C20, 17C60 (Secondary) ,Rings and Algebras (math.RA) ,010201 computation theory & mathematics ,Simple (abstract algebra) ,FOS: Mathematics ,Isomorphism ,0101 mathematics ,Abelian group ,Equivalence (measure theory) ,Real number ,Mathematics - 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., Comment: 24 pages
- Published
- 2019