Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of differentials and Cartan calculus on bicrossproducts   We provide the Cartan calculus for bicovariant differential forms on
bicrossproduct quantum groups $k(M)\lrbicross kG$ associated to finite group
factorizations $X=GM$ and a field $k$. The irreducible calculi are associated
to certain conjugacy classes in $X$ and representations of isotropy groups. We
find the full exterior algebras and show that they are inner by a bi-invariant
1-form $\theta$ which is a generator in the noncommutative de Rham cohomology
$H^1$. The special cases where one subgroup is normal are analysed. As an
application, we study the noncommutative cohomology on the quantum codouble
$D^*(S_3)\isom k(S_3)\lrbicross k\Z_6$ and the quantum double
$D(S_3)=k(S_3)\lcross kS_3$, finding respectively a natural calculus and a
unique calculus with $H^0=k.1$.

30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs