Arithmetic differential equations on $G{L}_n$, II: arithmetic Lie theory

Abstract

Motivated by the search of a concept of linearity in the theory of arithmetic differential equations we introduce here an arithmetic analogue of Lie algebras and a concept of skew arithmetic differential cocycles. We will then construct such skew cocycles, based on certain remarkable lifts of Frobenius for the classical groups $G{L}_n,S{L}_n,S{O}_n,S{p}_n$. The theory for $G{L}_n$, especially on the Galois side, will be further developed in a sequel to this paper.

References in corpus (1)

• Arithmetic differential equations on $G{L}_n$, I: differential cocycles

Cited by in corpus (2)

• Transcendental numbers as solutions to arithmetic differential equations
• Arithmetic analogues of some basic concepts from Riemannian geometry