Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards a noncommutative Picard-Vessiot theory   A Chen generating series, along a path and with respect to $m$ differential
forms,is a noncommutative series on $m$ letters and with coefficients which are
holomorphic functionsover a simply connected manifold in other words a series
with variable (holomorphic) coefficients.Such a series satisfies a first order
noncommutative differential equation which is considered, bysome authors, as
the universal differential equation, (i.e.) universality can beseen by
replacing each letter by constant matrices (resp. analytic vector fields)and
then solving a system of linear (resp. nonlinear) differential equations.Via
rational series, on noncommutative indeterminates and with coefficients in
rings, andtheir non-trivial combinatorial Hopf algebras, we give the first step
of a noncommutativePicard-Vessiot theory and we illustrate it with the case of
linear differential equationswith singular regular singularities thanks to the
universal equation previously mentioned.

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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: stat