|XXVIII Workshop on Geometric Methods in Physics||28.06-04.07.2009|
Simple graded commutative algebras
We study the notion of Gamma-graded commutative algebra for an arbitrary abelian group Gamma. We prove that the Clifford algebras are the only simple (real or complex) finite-dimensional associative graded commutative algebras. Our approach also leads to non-associative graded commutative algebras extending the Clifford algebras.
This is a joint work with Sophie Morier-Genoud.