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Artículo
On the bracket of integrable derivations
(Elsevier, 2021-05-15)
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 ...
Artículo
On the modules of m-integrable derivations in non-zero characteristic
(Elsevier, 2012-03-20)
Let k be a commutative ring and A a commutative k-algebra. Given a positive integer m, or m = ∞, we say that a k-linear derivation δ of A is m-integrable if it extends up to a Hasse–Schmidt derivation D = (Id, D1 = δ, ...
Artículo
Rings of differential operators as enveloping algebras of Hasse–Schmidt derivations
(Elsevier, 2020-01)
Let k be a commutative ring and A a commutative k-algebra. In this paper we introduce the notion of enveloping algebra of Hasse–Schmidt derivations of A over k and we prove that, under suitable smoothness hypotheses, the ...