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arXiv · 1709.03833

Revisiting Clifford Algebras

Marc Atteia
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Abstract

This paper is divided in three parts. In the first part, I study the Clifford algebra associated to the hessian of a functional $f$ defined on an open subset of $\mathbb{R}^n$ \ and the Clifford algebra associated to the hessian of the Legendre transform of $f$. I give also the definition of a tensorial topology on a Clifford algebra. In the second part, I study the Clifford algebra $C\left( E,q\right) $ of an infinite dimensional Banach space $E$ and its main properties. Finally, in the third part, I give the explicit formula of the hilbertian kernel of a Clifford algebra with examples.

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Marc Atteia. 2017-08-16. Revisiting Clifford Algebras. https://arxiv.org/abs/1709.03833

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