Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pointed Hopf Algebras with Triangular Decomposition -- A
  Characterization of Multiparameter Quantum Groups   In this paper, we present an approach to the definition of multiparameter
quantum groups by studying Hopf algebras with triangular decomposition.
Classifying all of these Hopf algebras which are of what we call weakly
separable type over a group, we obtain a class of pointed Hopf algebras which
can be viewed as natural generalizations of multiparameter deformations of
universal enveloping algebras of Lie algebras. These Hopf algebras are
instances of a new version of braided Drinfeld doubles, which we call
asymmetric braided Drinfeld doubles. This is a generalization of an earlier
result by Benkart and Witherspoon (2004) who showed that two-parameter quantum
groups are Drinfeld doubles. It is possible to recover a Lie algebra from these
doubles in the case where the group is free abelian and the parameters are
generic. The Lie algebras arising are generated by Lie subalgebras isomorphic
to sl2.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin