Isotropy quotients of Hopf algebroids and the fundamental groupoid of digraphs

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 ideals and isotropy quotients for arbitrary Hopf algebroids. Using these ingredients, we prove a Riemann-Hilbert correspond...

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Bibliographic Details
Published in:Journal of algebra 2022-11, Vol.610, p.591-631
Main Author: Ghobadi, Aryan
Format: Article
Language:English
Subjects:
Bialgebroid
Bimodule connection
Directed graphs
Fundamental group
Groupoids
Hopf algebroid
Noncommutative geometry
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Summary: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 ideals and isotropy quotients for arbitrary Hopf algebroids. Using these ingredients, we prove a Riemann-Hilbert correspondence for digraphs, by showing that the groupoid algebra of the fundamental groupoid of a digraph is isomorphic to the isotropy quotient of the Hopf algebroid corresponding to flat connections over the digraph.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2022.07.036