Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bicocycle Double Cross Constructions   We introduce the notion of a bicocycle double cross product (resp. sum) Lie
group (resp. Lie algebra), and a bicocycle double cross product bialgebra,
generalizing the unified products. On the level of Lie groups the construction
yields a Lie group on the product space of two pointed manifolds, none of which
being necessarily a subgroup. On the level of Lie algebras, similarly, a Lie
algebra is obtained on the direct sum of two vector spaces, none of which is
required to be a subalgebra. Finally, on the quantum level the theory presents
a bialgebra, on the tensor product of two (co)algebras that are not necessarily
sub-bialgebras, the semidual of which being a cocycle bicrossproduct bialgebra.

1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex