Simple graded commutative algebras

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Date
2009-03-06MFO Scientific Program
Research in Pairs 2009Series
Oberwolfach Preprints;2009,12Author
Morier-Genoud, Sophie
Ovsienko, Valentin
Metadata
Show full item recordOWP-2009-12
Abstract
We study the notion of $\Gamma$-graded commutative algebra for an arbitrary abelian group $\Gamma$. The main examples are the Clifford algebras already treated in [2]. We prove that the Clifford algebras are the only simple finite-dimensional associative graded commutative algebras over $\mathbb{R}$ or $\mathbb{C}$. Our approach also leads to non-associative graded commutative algebras extending the Clifford algebras.