Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting Clifford Algebras   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.

7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc