Towards differentiation and integration between Hopf algebroids and Lie algebroids
Ardizzoni, Alessandro (University of Turin, Department of Mathematics "Giuseppe Peano")
El Kaoutit, Laiachi (Universidad de Granada. Departamento de Álgebra)
Saracco, Paolo (Université libre de Bruxelles. Département de Mathématique)

Fecha:	2023
Resumen:	In this paper we set up the foundations around the notions of formal differentiation and formal integration in the context of commutative Hopf algebroids and Lie-Rinehart algebras. Specifically, we construct a contravariant functor from the category of commutative Hopf algebroids with a fixed base algebra to that of Lie-Rinehart algebras over the same algebra, the differentiation functor, which can be seen as an algebraic counterpart to the differentiation process from Lie groupoids to Lie algebroids. The other way around, we provide two interrelated contravariant functors from the category of Lie-Rinehart algebras to that of commutative Hopf algebroids, the integration functors. One of them yields a contravariant adjunction together with the differentiation functor. Under mild conditions, essentially on the base algebra, the other integration functor only induces an adjunction at the level of Galois Hopf algebroids. By employing the differentiation functor, we also analyse the geometric separability of a given morphism of Hopf algebroids. Several examples and applications are presented.
Ayudas:	Ministerio de Economía y Competitividad MTM2016-77033-P
Nota:	Research supported by the Spanish Ministerio de Economía y Competitividad and the European Union, grant MTM2016-77033-P. Paolo Saracco is a Chargé de Recherches of the Fonds de la Recherche Scientifique - FNRS. This paper was written while the first and third authors were members of the National Group for Algebraic and Geometric Structures and their Applications (GNSAGA-INdAM).
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; Versió publicada
Materia:	(co)commutative hopf algebroids ; Affine groupoid schemes ; Differentiation and integration ; Kähler module ; Lie-rinehart algebras ; Lie algebroids ; Lie groupoids ; Malgrange groupoids ; Finite dual ; Tannaka reconstruction
Publicado en:	Publicacions matemàtiques, Vol. 67 Núm. 1 (2023) , p. 3-88 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/412620
DOI: 10.5565/PUBLMAT6712301

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