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Hopf algebroids and quantum groupoids

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arxiv q-alg/9505024 v1 pith:OWMBHJOW submitted 1995-05-19 q-alg math.QA

Jiang-Hua Lu (University of Arizona) This is my paper · ORCID
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keywords algebrashopfquantumalgebroidsgroupoidswhenappliedassociated
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abstract

We introduce the notion of Hopf algebroids, in which neither the total algebras nor the base algebras are required to be commutative. We give a class of Hopf algebroids associated to module algebras of the Drinfeld doubles of Hopf algebras when the $R$-matrices act properly. When this construction is applied to quantum groups, we get examples of quantum groupoids, which are semi-classical limits of Poisson groupoids. The example of quantum $sl(2)$ is worked out in details.

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Forward citations

Cited by 2 Pith papers

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  1. Backward error analysis for matrix discretizations of 2-D Euler equations

    math.NA 2026-07 accept novelty 8.0 of 10

    ISOSYRK methods on Zeitlin’s Euler–Zeitlin system admit n-independent exponentially small modified-Hamiltonian errors for times exp(c/ε) when h = ε ℏ_n.

  2. Examples of scalar extension Hopf algebroids over a universal enveloping algebra

    math.QA 2025-06 accept novelty 5.0 of 10

    For a finite-dimensional Lie algebra g, U(g) is a braided commutative Yetter-Drinfeld module algebra over any Hopf algebra H containing the adjoint matrix coefficients, making H smash U(g) a scalar extension Hopf alge...

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