Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reworking on affine exterior algebra of Grassmann, Peano and his school   In this paper a construction of affine exterior algebra of Grassmann, with a
special attention to the revisitation of this subject operated by Peano and his
School, is examined from a historical viewpoint. Even if the exterior algebra
over a vector space is a well known concept, the construction of an exterior
algebra over an affine space, in which points and vectors coexist, has been
neglected. This paper wants to fill this lack.
  Some attention is given to the introduction of defining by abstraction (today
called definition by quotienting or by equivalence relation), a procedure due
to and used by Peano to define geometric forms, basic elements of an affine
exterior algebra. This Peano's innovative way of defining, is a relevant
contribution to mathematics.
  It is observed that in the construction of an affine exterior algebra on the
Euclidean three-dimensional space, Grassmann and Peano make use of metric
concepts: an accurate analysis shows that, in some cases, the metric aspects
can be eliminated, putting into evidence the sufficiency of the underlying
affine structure of the Euclidean space.
  In the final part of the paper some geometrical and mechanical applications
and interpretations of the affine exterior algebra given by Grassmann and Peano
are presented.

6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin