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Examples of Weak Hopf Algebras Arising from Vacant Double Groupoids

Published online by Cambridge University Press:  11 January 2016

Nicolás Andruskiewitsch  and
Juan Martín Mombelli
Nicolás Andruskiewitsch
Affiliation:
Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM - CONICET, Medina Allende s/n, (5000) Ciudad Universitaria, Córdoba, [email protected]
Juan Martín Mombelli
Affiliation:
Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM - CONICET, Medina Allende s/n, (5000) Ciudad Universitaria, Córdoba, [email protected]
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Abstract

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We construct explicit examples of weak Hopf algebras (actually face algebras in the sense of Hayashi [H]) via vacant double groupoids as explained in [AN]. 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.

Keywords

17B3781R50
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 181 , March 2006 , pp. 1 - 27
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

References

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