Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clifford Algebras, Clifford Groups, and a Generalization of the
  Quaternions   One of the main goals of these notes is to explain how rotations in reals^n
are induced by the action of a certain group, Spin(n), on reals^n, in a way
that generalizes the action of the unit complex numbers, U(1), on reals^2, and
the action of the unit quaternions, SU(2), on reals^3 (i.e., the action is
defined in terms of multiplication in a larger algebra containing both the
group Spin(n) and reals^n). The group Spin(n), called a spinor group, is
defined as a certain subgroup of units of an algebra, Cl_n, the Clifford
algebra associated with reals^n.
  Since the spinor groups are certain well chosen subgroups of units of
Clifford algebras, it is necessary to investigate Clifford algebras to get a
firm understanding of spinor groups. These notes provide a tutorial on Clifford
algebra and the groups Spin and Pin, including a study of the structure of the
Clifford algebra Cl_{p, q} associated with a nondegenerate symmetric bilinear
form of signature (p, q) and culminating in the beautiful "8-periodicity
theorem" of Elie Cartan and Raoul Bott (with proofs).

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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol