arXiv subjects

L. Narváez-Macarro

Publications and source records attributed to L. Narváez-Macarro.

3 recordsLinked to original sources

arXiv2020

Hasse--Schmidt derivations versus classical derivations

In this paper we survey the notion and basic results on multivariate Hasse--Schmidt derivations over arbitrary commutative algebras and we associate to such an object a family of classical derivations. We study the behavior of these derivations under the action of substitution maps and we prove that, in characteristic $0$, the original multivariate Hasse--Schmidt derivation can be recovered from the associated family of classical derivations. Our constructions generalize a previous one by M. Mirzavaziri in the case of a base field of characteristic $0$.

math.AG↗

arXiv2019

Rings of differential operators as enveloping algebras of Hasse--Schmidt derivations

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 canonical map from the above enveloping algebra to the ring of differential operators $\mathcal{D}_{A/k}$ is an isomorphism. This result generalizes the characteristic 0 case in which the ring $\mathcal{D}_{A/k}$ appears as the enveloping algebra of the Lie-Rinehart algebra of the usual $k$-derivations of $A$ provided that $A$ is smooth over $k$.

math.AG↗

arXiv2019

Hasse--Schmidt modules versus integrable connections

We prove that, in characteristic 0, any Hasse-Schmidt module structure can be recovered from its underlying integrable connection, and consequently Hasse--Schmidt modules and modules endowed with an integrable connection coincide.

math.AG↗