Hopf algebroids and quantum groupoids

Details Hopf algebroids and quantum groupoids Hopf algebroids and quantum groupoids

1995-05-19

arxiv.org/abs/q-alg/9505024v1

Mathematics

Quantum Algebra

30 pages, in Latex

Scientific paper

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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