On d-solvability for linear differential equations

摘要

The aim of this paper is to investigate the possibility of solving a linear differential equation of degree n by means of differential equations of degree less than or equal to a fixed d, 1 ≤ d ≤ n. This paper recovers and extends work of G. Fano, M. F. Singer and E. Compoint. Representations of algebraic Lie algebras are the main tool.