Gradings on semisimple algebras
Alejandra S. C\'ordova-Mart\'inez, Alberto Elduque

TL;DR
This paper classifies gradings by abelian groups on semisimple nonassociative algebras, reducing the problem to simple algebras using loop algebras and introducing a new approach to group-gradings.
Contribution
It introduces a framework for understanding gradings on semisimple algebras by connecting them to simple algebras via loop algebras and defining free products of group-gradings.
Findings
Reduction of grading classification to simple algebras
Development of a definition for free products of group-gradings
Application of loop algebras in grading classification
Abstract
The classification of gradings by abelian groups on finite direct sums of simple finite-dimensional nonassociative algebras over an algebraically closed field is reduced, by means of the use of loop algebras, to the corresponding problem for simple algebras. This requires a good definition of (free) products of group-gradings.
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