Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braided affine geometry and q-analogs of wave operators   The main goal of this review is to compare different approaches to
constructing geometry associated with a Hecke type braiding (in particular,
with that related to the quantum group U_q(sl(n))). We make an emphasis on
affine braided geometry related to the so-called Reflection Equation Algebra
(REA). All objects of such type geometry are defined in the spirit of affine
algebraic geometry via polynomial relations on generators.
  We begin with comparing the Poisson counterparts of "quantum varieties" and
describe different approaches to their quantization. Also, we exhibit two
approaches to introducing q-analogs of vector bundles and defining the
Chern-Connes index for them on quantum spheres. In accordance with the
Serre-Swan approach, the q-vector bundles are treated as finitely generated
projective modules over the corresponding quantum algebras.
  Besides, we describe the basic properties of the REA used in this
construction and compare different ways of defining q-analogs of partial
derivatives and differentials on the REA and algebras close to them. In
particular, we present a way of introducing a q-differential calculus via
Koszul type complexes. The lements of the q-calculus are applied to defining
q-analogs of some relativistic wave operators.

25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci