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On nonassociative graded-simple algebras over the field of real numbers. (English) Zbl 1429.17006

Andruskiewitsch, Nicolás (ed.) et al., Tensor categories and Hopf algebras. Scientific session of the Mathematical Congress of the Americas ‘Hopf algebras and tensor categories’, Montreal, Canada, July 27–28, 2017. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 728, 25-48 (2019).
Summary: 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.
For the entire collection see [Zbl 1415.18001].

MSC:

17A60 Structure theory for nonassociative algebras
17D05 Alternative rings
17C20 Simple, semisimple Jordan algebras
17C60 Division algebras and Jordan algebras
16W50 Graded rings and modules (associative rings and algebras)
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