Graded commutative algebras: examples, classification, open problems
Sophie Morier-Genoud (IMJ), Valentin Ovsienko (ICJ)

TL;DR
This paper explores $ ext{G}$-graded commutative algebras, providing examples, a classification result, and posing an open problem to advance understanding of their structure and properties.
Contribution
It offers a unifying perspective on $ ext{G}$-graded commutative algebras, including examples like quaternions and Clifford algebras, along with a recent classification and an open problem.
Findings
Classification of $ ext{G}$-graded commutative algebras
Examples including quaternions and Clifford algebras
Formulation of an open problem in the field
Abstract
We consider -graded commutative algebras, where is an abelian group. Starting from a remarkable example of the classical algebra of quaternions and, more generally, an arbitrary Clifford algebra, we develop a general viewpoint on the subject. We then give a recent classification result and formulate an open problem.
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