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Weak multiplier bialgebras


Authors: Gabriella Böhm, José Gómez-Torrecillas and Esperanza López-Centella
Journal: Trans. Amer. Math. Soc. 367 (2015), 8681-8721
MSC (2010): Primary 16T05, 16T10, 16D90, 18B40
DOI: https://doi.org/10.1090/tran/6308
Published electronically: April 9, 2015
MathSciNet review: 3403069
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Abstract: A non-unital generalization of weak bialgebra is proposed with a multiplier-valued comultiplication. Certain canonical subalgebras of the multiplier algebra (named the `base algebras') are shown to carry coseparable co-Frobenius coalgebra structures. Appropriate modules over a nice enough weak multiplier bialgebra are shown to constitute a monoidal category via the (co)module tensor product over the base (co)algebra. The relation to Van Daele and Wang's (regular and arbitrary) weak multiplier Hopf algebra is discussed.


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Additional Information

Gabriella Böhm
Affiliation: Wigner Research Centre for Physics, P.O.B. 49, H-1525 Budapest 114, Hungary
Email: bohm.gabriella@wigner.mta.hu

José Gómez-Torrecillas
Affiliation: Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain
Email: gomezj@ugr.es

Esperanza López-Centella
Affiliation: Departamento de Álgebra, Universidad de Granada, E-18071 Granada, Spain
Email: esperanza@ugr.es

DOI: https://doi.org/10.1090/tran/6308
Received by editor(s): June 6, 2013
Received by editor(s) in revised form: October 25, 2013
Published electronically: April 9, 2015
Additional Notes: This research was partially supported by the Spanish Ministerio de Ciencia en Innovación and the European Union, grant MTM2010-20940-C02-01, by the Hungarian Scientific Research Fund OTKA, grant K108384, and by the Nefim Fund of Wigner RCP. The authors thank Alfons Van Daele for valuable discussions from which this paper benefits a lot.
Article copyright: © Copyright 2015 American Mathematical Society