Hostname: page-component-84b7d79bbc-g7rbq Total loading time: 0 Render date: 2024-07-30T23:34:26.675Z Has data issue: false hasContentIssue false
  • English
  • Français

WEAK BRAIDED BIALGEBRAS AND WEAK ENTWINING STRUCTURES

Part of: Categories with structure

Published online by Cambridge University Press:  27 July 2009

J. N. ALONSO ÁLVAREZ ,
J. M. FERNÁNDEZ VILABOA  and
R. GONZÁLEZ RODRÍGUEZ
J. N. ALONSO ÁLVAREZ
Affiliation:
Departamento de Matemáticas, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, E-36280 Vigo, Spain (email: jnalonso@uvigo.es)
J. M. FERNÁNDEZ VILABOA
Affiliation:
Departamento de Álxebra, Universidad de Santiago de Compostela, E-15771 Santiago de Compostela, Spain (email: alvila@usc.es)
R. GONZÁLEZ RODRÍGUEZ*
Affiliation:
Departamento de Matemática Aplicada II, Universidad de Vigo, Campus Universitario Lagoas-Marcosende, E-36310 Vigo, Spain (email: rgon@dma.uvigo.es)
*
✉For correspondence; e-mail: rgon@dma.uvigo.es
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we clarify and improve the notion of weak braided bialgebra using weak entwining structures. As a main result we show that the notion of weak braided bialgebra can be rewritten in terms of weak entwining structures.

Keywords

monoidal categoryweak braided hopf algebraentwining structures

MSC classification

Secondary: 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 2 , October 2009 , pp. 306 - 316
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

The authors have been supported by Ministerio de Educación, Xunta de Galicia and by FEDER, Projects: MTM2007-62427, MTM2006-14908-CO2-01, PGIDT07PXB322079PR.

References

[1] Alonso Álvarez, J. N., Fernández Vilaboa, J. M. and González Rodríguez, R., ‘Weak Hopf algebras and weak Yang–Baxter operators’, J. Algebra 320 (2008), 2101–2143.Google Scholar
[2] Alonso Álvarez, J. N., Fernández Vilaboa, J. M. and González Rodríguez, R., ‘Weak braided Hopf algebras’, Indiana Univ. Math. J. 57 (2008), 2423–2458.Google Scholar
[3] Beck, J., ‘Distributive laws’, in: Seminar on Triples and Categorical Homology Theory, Lecture Notes in Mathematics, 80 (ed. B. Eckmann) (Springer, Berlin, 1969), pp. 119–140.CrossRefGoogle Scholar
[4] Böhm, G., Nill, F. and Szlachányi, K., ‘Weak Hopf algebras, I. Integral theory and C *-structure’, J. Algebra 221 (1999), 385–438.CrossRefGoogle Scholar
[5] Caenepeel, S. and De Groot, E., ‘Modules over weak entwining structures’, in: New Trends in Hopf Algebra Theory, Contemporary Mathematics, 267 (American Mathematical Society, Providence, RI, 2000), pp. 31–54.CrossRefGoogle Scholar
[6] Joyal, A. and Street, R., ‘Braided tensor categories’, Adv. Math. 102 (1993), 20–78.CrossRefGoogle Scholar
[7] Majid, S., ‘Algebras and Hopf algebras in braided categories’, in: Advances in Hopf Algebras, Lecture Notes in Pure and Applied Mathematics, 158 (Marcel Dekker, New York, 1994), pp. 55–105.Google Scholar
[8] Majid, S., ‘Cross products by braided groups and bosonization’, J. Algebra 163 (1994), 165–190.Google Scholar
[9] Pastro, C. and Street, R., ‘Weak Hopf monoids in braided monoidal categories’, Algebra and Number Theory, at press (2008).Google Scholar
[10] Radford, D. E., ‘The structure of Hopf algebras with a projection’, J. Algebra 92 (1985), 322–347.Google Scholar
[11] Takeuchi, M., ‘Survey of braided Hopf algebras’, in: New Trends in Hopf Algebra Theory, Contemporary Mathematics, 267 (American Mathematical Society, Providence, RI, 2000), pp. 301–323.CrossRefGoogle Scholar