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Simple graded commutative algebras

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 نشر من قبل Valentin Ovsienko
 تاريخ النشر 2009
  مجال البحث
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We study the notion of $Gamma$-graded commutative algebra for an arbitrary abelian group $Gamma$. The main examples are the Clifford algebras already treated by Albuquerque and Majid. 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.



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