Hopf algebroids and quantum groupoids

Jiang-Hua Lu

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arXiv · q-alg/9505024

Hopf algebroids and quantum groupoids

Jiang-Hua Lu

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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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BibTeX RIS

Jiang-Hua Lu. 1995-05-19. Hopf algebroids and quantum groupoids. https://arxiv.org/abs/q-alg/9505024

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