论文标题
迈向非交流性的Picard-vessiot理论
Towards a noncommutative Picard-Vessiot theory
论文作者
论文摘要
在$ m $差异形式方面，陈述系列的系列是在$ m $字母上的非交换系列，其系数具有全态函数，换句话说是一个简单地连接的歧管，换句话说，具有可变（holomorthic）系数的系列系列。 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由于前面提到的通用方程式，它具有线性微分方程的情况，具有奇异的常规奇异性。
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.
