36 citations · 84 across the 14 of their papers we have counts for
17 papers
Correspondence theorems for Hopf algebroids with applications to affine groupoids
Laiachi El Kaoutit, Aryan Ghobadi, Paolo Saracco +1
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 con…
The Hopf algebroid structure of differentially recursive sequences
Laiachi El Kaoutit, Paolo Saracco
A differentially recursive sequence over a differential field is a sequence of elements satisfying a homogeneous differential equation with non-constant coefficients (namely, Taylo…
On Burnside Theory for groupoids
Laiachi El Kaoutit, Leonardo Spinosa
We explore the concept of conjugation between subgroupoids, providing several characterizations of the conjugacy relation (Theorem A in §1.2). We show that two finite groupoid-sets…
Mackey formula for bisets over groupoids
Laiachi El Kaoutit, Leonardo Spinosa
In this paper we establish the Mackey formula for groupoids, extending the well known formula in abstract groups context. This formula involves the notion of groupoid-biset, its or…
Comparing topologies on linearly recursive sequences
Laiachi El Kaoutit, Paolo Saracco
The space of linearly recursive sequences of complex numbers admits two distinguished topologies. Namely, the adic topology induced by the ideal of those sequences whose first term…
Topological tensor product of bimodules, complete Hopf Algebroids and convolution algebras
Laiachi El Kaoutit, Paolo Saracco
Given a finitely generated and projective Lie-Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between the completion of th…
Finite dual of a cocommutative Hopf algebroid. Application to linear differential matrix equations and Picard-Vessiot theory
Laiachi El Kaoutit, José Gómez-Torrecillas
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 t…
On geometrically transitive Hopf algebroids
Laiachi El Kaoutit
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 a…
Functorial Constructions for Non-associative Algebras with Applications to Quasi-bialgebras
Alessandro Ardizzoni, Laiachi El Kaoutit, Paolo Saracco
The aim of this paper is to establish a contravariant adjunction between the category of quasi-bialgebras and a suitable full subcategory of dual quasi-bialgebras, adapting the not…
Morita theory for Hopf algebroids, principal bibundles, and weak equivalences
Laiachi El Kaoutit, Niels Kowalzig
We show that two flat commutative Hopf algebroids are Morita equivalent if and only if they are weakly equivalent and if and only if there exists a principal bibundle connecting th…
Representative functions on discrete groupoids and duality with Hopf algebroids
Laiachi EL Kaoutit
The aim of this paper is to establish a duality between the category of discrete groupoids and the category of geometrically transitive commutative Hopf algebroids in the sense of…
Invertible Bimodules, Miyashita Action in Monoidal Categories and Azumaya Monoids
Alessandro Ardizzoni, Laiachi El Kaoutit
In this paper we introduce and study Miyashita action in the context of monoidal categories aiming by this to provide a common framework of previous studies in the literature. We m…
Morita base change in Hopf-cyclic (co)homology
Laiachi El Kaoutit, Niels Kowalzig
In this paper, we establish the invariance of cyclic (co)homology of left Hopf algebroids under the change of Morita equivalent base algebras. The classical result on Morita invari…
Invertible unital bimodules over rings with local units, and related exact sequences of groups II
L. EL Kaoutit, J. Gómez-Torrecillas
Let be a ring with a set of local units, and a homomorphism of groups $\underlineΘ : \G \to \Picar{R}$ to the Picard group of . We study under which conditions …
Categories of comodules and chain complexes of modules
A. Ardizzoni, L. El Kaoutit, C. Menini
Let $\lL(A)$ denote the coendomorphism left -bialgebroid associated to a left finitely generated and projective extension of rings with identities. We show that the ca…
The bicategories of corings
Tomasz Brzezinski, L El Kaoutit, J Gomez-Torrecillas
To a B-coring and a (B,A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a cor…
Semisimple corings
L. El Kaoutit, J. Gomez-Torrecillas, F. J. Lobillo
While semisimple artinian rings and semisimple coalgebras over a field can be described in terms of matrices (either matrix ring over division rings or comatrix coalgebras over the…