These notes provide a self-contained introduction to Lie algebroids, Lie-Rinehart algebras
and their universal envelopes. This review is motivated by the speculation that higher-spin …

We extend a theorem, originally formulated by Blattner-Cohen-Montgomery for crossed
products arising from Hopf algebras weakly acting on noncommutative algebras, to the …

We provide a correspondence between one-sided coideal subrings and one-sided ideal two-
sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional …

On anchored Lie algebras and the Connes–Moscovici bialgebroid construction Page 1 J.
Noncommut. Geom. 16 (2022), 1007–1053 DOI 10.4171/JNCG/475 © 2022 European …

The main aim of this paper is to give a Hopf algebroid approach to the Picard-Vessiot theory
of linear differential matrix equations with coefficients in the polynomial complex algebra. To …

We prove how the universal enveloping algebra constructions for Lie–Rinehart algebras
and anchored Lie algebras are naturally left adjoint functors. This provides a conceptual …

Action Lie groupoids are used to model spaces of orbits of actions of Lie groups on
manifolds. For each such action groupoid M⋊ H, we construct a locally convex bialgebroid …

A differentially recursive sequence over a differential field is a sequence of elements
satisfying a homogeneous differential equation with non-constant coefficients (namely …

In this paper we investigate the formal notions of differentiation and integration in the context
of commutative Hopf algebroids and Lie algebroid, or more precisely Lie-Rinehart algebras …

A fundamental tool of Differential Galois Theory is the assignment of an algebraic group to
each finite-dimensional differential module over differential field in such a way that the …