Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On monoidal autoequivalences of the category of Yetter-Drinfeld modules
  over a group: The lazy case   An interesting open question is to determine the group of monoidal
autoequivalences of the category of Yetter-Drinfeld modules over a finite group
$G$, or equivalently the group of Bigalois objects over the dual of the
Drinfeld double $DG$. In particular one would hope to decompose this group into
terms related to monoidal autoequivalences for the group algebra, the dual
group algebra and interaction terms.
  We report on our progress in this question: We first prove a decomposition of
the group of Hopf algebra automorphisms of the Drinfeld double into three
subgroups, which reduces in the case $G=\mathbb{Z}_p^n$ to a Bruhat
decomposition of $\mathrm{GL}_{2n}(\mathbb{Z}_p)$. Secondly, we propose a
Kuenneth-like formula for the Hopf algebra cohomology of $DG^*$ into three
terms and prove partial results in the case of lazy cohomology. We use these
results for the calculation of the Brauer-Picard group in the lazy case in
[LP15].

22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph