On the bracket of integrable derivations

Abstract

We prove that any multi-variate Hasse-Schmidt derivation can be decomposed in terms of substitution maps and uni-variate Hasse-Schmidt derivations. As a consequence we prove that the bracket of two $m$-integrable derivations is also $m$-integrable, for $m$ a positive integer or infinity.

References in corpus (5)

• On the modules of m-integrable derivations in non-zero characteristic
• Hasse--Schmidt derivations, divided powers and differential smoothness
• On Hasse--Schmidt derivations: the action of substitution maps
• Integrable derivations in the sense of Hasse-Schmidt for some binomial plane curve
• Leaps of modules of integrable derivations in the sense of Hasse-Schmidt