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Difference Galois theory of linear differential equations (1302.7198v2)
Published 28 Feb 2013 in math.AC, math.AG, math.DS, and math.RA
Abstract: We develop a Galois theory for linear differential equations equipped with the action of an endomorphism. This theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation. The Galois groups here are linear difference algebraic groups, i.e., matrix groups defined by algebraic difference equations.