Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A prelie algebra associated to a linear endomorphism and related
  algebraic structures   We attach to any linear endomorphism f of any vector space V a structure of
prelie algebra on the shuffle algebra T(V); we describe its enveloping algebra,
the dual Hopf algebra and the associated group of characters. For f=Id\_V, we
find the algebra of formal diffeomorphisms, seen as a subalgebra of the
Connes-Kreimer Hopf algebra of rooted trees in the context of QFT; for other
well-chosen f, we obtain the groups of Fliess operators in Control Theory. An
algebraic structures of these Com-Prelie Hopf algebras is carried out:
gradations, group of automorphisms, subobject generated by V, etc.

37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th