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 …

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 …

This paper contributes to the characterization of a certain class of commutative Hopf
algebroids. It is shown that a commutative flat Hopf algebroid with a non zero base ring and …

Mackey formula for bisets over groupoids Page 1 Journal of Algebra and Its Applications Vol.
18, No. 6 (2019) 1950109 (35 pages) c World Scientific Publishing Company DOI: 10.1142/S0219498819501093 …

Algebraic Structures in Noncommutative Geometry: A Study of Hopf Algebras, Hopf-Galois
Extensions, and Hopf Algebroids Page 1 Mathematics Area - PhD course in Geometry and …

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 …

We construct a contravariant functor (the finite dual functor) from the category of co-
commutative Hopf algebroids to the category of commutative Hopf algebroids. Using this …

Given a morphism of (small) groupoids with injective object map, we provide sufficient and
necessary conditions under which the induction and co-induction functors between the …

We explore the category of internal categories in the usual category of (right) group-sets,
whose objects are referred to as categorified group-sets. More precisely, we develop a new …