7 citations · 15 across the 7 of their papers we have counts for
7 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…
Hopf Monads: A Survey with New Examples and Applications
Aryan Ghobadi
We survey the theory of Hopf monads on monoidal categories, and present new examples and applications. As applications, we utilise this machinery to present a new theory of cross p…
Isotopy Quotients of Hopf Algebroids and the Fundamental Groupoid of Digraphs
Aryan Ghobadi
We build on our construction of Hopf algebroids from noncommutative calculi under the further assumption of surjectivity for the calculus. We also introduce the notions of Hopf ide…
Drinfeld Twists on Skew Braces
Aryan Ghobadi
We introduce the notion of Drinfeld twists for both set-theoretical YBE solutions and skew braces. We give examples of such twists and show that all twists between skew braces come…
Skew Braces as Remnants of Co-quasitriangular Hopf Algebras in
Aryan Ghobadi
Skew braces have recently attracted attention as a method to study set-theoretical solutions of the Yang-Baxter equation. Here, we present a new approach to these solutions by stud…
Pivotal Objects in Monoidal Categories and Their Hopf Monads
Aryan Ghobadi
An object in a monoidal category is called pivotal if its left dual and right dual objects are isomorphic. Given such an object and a choice of dual , we const…
Hopf Algebroids, Bimodule Connections and Noncommutative Geometry
Aryan Ghobadi
We construct new examples of left bialgebroids and Hopf algebroids, arising from noncommutative geometry. Given a first order differential calculus on an algebra , with the…