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| Detailed view | Preprint, Working Paper, ... |
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| Available versions: | v1 (2009-04-18) | v2 (2009-04-19) | v3 (2009-05-07) |
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| Simple graded commutative algebras |
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| Sophie Morier-Genoud1Valentin Ovsienko2 |
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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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| 1: | IMJ - Institut de Mathématiques de Jussieu |
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| 2: | ICJ - Institut Camille Jordan |
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| hal-00376589, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00376589 | |
| oai:hal.archives-ouvertes.fr:hal-00376589 | |
| From: Valentin Ovsienko | |
| Submitted on: Sunday, 19 April 2009 17:55:40 | |
| Updated on: Sunday, 19 April 2009 21:07:41 | |
