Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non commutative finite dimensional manifolds II. Moduli space and
  structure of non commutative 3-spheres   This paper contains detailed proofs of our results on the moduli space and
the structure of noncommutative 3-spheres. We develop the notion of central
quadratic form for quadratic algebras, and a general theory which creates a
bridge between noncommutative differential geometry and its purely algebraic
counterpart. It allows to construct a morphism from an involutive quadratic
algebras to a C*-algebra constructed from the characteristic variety and the
hermitian line bundle associated to the central quadratic form. We apply the
general theory in the case of noncommutative 3-spheres and show that the above
morphism corresponds to a natural ramified covering by a noncommutative
3-dimensional nilmanifold. We then compute the Jacobian of the ramified
covering and obtain the answer as the product of a period (of an elliptic
integral) by a rational function. We describe the real and complex moduli
spaces of noncommutative 3-spheres, relate the real one to root systems and the
complex one to the orbits of a birational cubic automorphism of three
dimensional projective space. We classify the algebras and establish duality
relations between them.

9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics