Examples of weak Hopf algebras arising from vacant double groupoids

Details Examples of weak Hopf algebras arising from vacant double groupoids Examples of weak Hopf algebras arising from vacant double groupoids

2004-05-19

arxiv.org/abs/math/0405374v1

Nagoya Math. J. 181 (2006), 1--27

Mathematics

Quantum Algebra

19 pages

Scientific paper

We construct explicit examples of weak Hopf algebras (actually face algebras in the sense of Hayashi) via vacant double groupoids as explained in \http://arxiv.org/abs/math.QA/0308228. To this end, we first study the Kac exact sequence for matched pairs of groupoids and show that it can be computed via group cohomology. Then we describe explicit examples of finite vacant double groupoids.

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