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dc.contributor.authorArdizzon, Alessandro
dc.contributor.authorEl Kaoutit Zerri, Laiachi 
dc.contributor.authorSaracco, Paolo
dc.identifier.citationA. Ardizzoni, L. El Kaoutit, P. Saracco. Diff and Int for Hopf and Lie Algebroids. Publ. Mat. 67 (2023), 3–88. [DOI: 10.5565/PUBLMAT6712301]es_ES
dc.description.abstractIn 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.es_ES
dc.description.sponsorshipSpanish Ministerio de Economía y Competitividades_ES
dc.description.sponsorshipEuropean Union MTM2016-77033-P.es_ES
dc.description.sponsorshipFonds de la Recherche Scientifique - FNRSes_ES
dc.description.sponsorshipNational Group for Algebraic and Geometric Structures and their Applications (GNSAGA-INdAM).es_ES
dc.description.sponsorshipUniversity of Turin PRX16/00108es_ES
dc.publisherUniversidad Autónoma de Barcelona, Dpto. de Matemáticas. Españaes_ES
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.subject(co)commutative Hopf algebroidses_ES
dc.subjectAffine groupoid schemeses_ES
dc.subjectDifferen- tiation and integrationes_ES
dc.subjectKähler modulees_ES
dc.subjectLie–Rinehart algebrases_ES
dc.subjectLie algebroidses_ES
dc.subjectLie groupoidses_ES
dc.subjectMalgrange groupoidses_ES
dc.subjectFinite duales_ES
dc.subjectTannaka reconstructiones_ES
dc.titleToward differentiation and integration between Hopf algebroids and Lie algebroidses_ES

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Attribution-NonCommercial-NoDerivatives 4.0 Internacional
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivatives 4.0 Internacional