Artículo
Di Luigi, C.; Guccione, J.A.; Guccione, J.J. "Brzezinski's crossed products and braided Hopf crossed products" (2004) Communications in Algebra. 32(9):3563-3580
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Abstract:
Recently, we introduced a notion of braided Hopf crossed product which generalizes the notion of classical Hopf crossed product defined independently by Blattner, Cohen and Montgomery and by Doi and Takeuchi. A very much general concept of crossed product is indebted to Brzeziriski. In this paper, we give a sufficient condition for a Brzezinski's crossed product be a braided Hopf crossed product. Majid prove that the quantum double of a quasitriangular Hopf algebra is isomorphic to a classical Hopf crossed product. As an application of our result we obtain a generalization of Majid's Theorem. Copyright © 2004 by Marcel Dekker, Inc.
Registro:
| Documento: | Artículo |
| Título: | Brzezinski's crossed products and braided Hopf crossed products |
| Autor: | Di Luigi, C.; Guccione, J.A.; Guccione, J.J. |
| Filiación: | Carlos Pellegrini, Buenos Aires, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón 1, Buenos Aires, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina |
| Palabras clave: | Crossed products; Hopf algebras |
| Año: | 2004 |
| Volumen: | 32 |
| Número: | 9 |
| Página de inicio: | 3563 |
| Página de fin: | 3580 |
| DOI: | http://dx.doi.org/10.1081/AGB-120039631 |
| Título revista: | Communications in Algebra |
| Título revista abreviado: | Commun. Algebra |
| ISSN: | 00927872 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00927872_v32_n9_p3563_DiLuigi |
Referencias:
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- Blattner, R.J., Cohen, M., Montgomery, S., Crossed products and inner actions of Hopf algebras (1986) Trans. Am. Math. Soc., 298, pp. 671-711
- Brzeziński, T., Crossed products by a coalgebra (1997) Comm. Alg., 25, pp. 3551-3575
- Cap, A., Schichl, H., Vanzura, J., On twisted tensor products of algebras (1995) Comm. Alg., 23, pp. 4701-4735
- Doi, Y., Takeuchi, M., Cleft comodule algebras by a bialgebra (1986) Comm. Alg., 14, pp. 801-817
- Guccione, J.A., Guccione, J.J., A generalization of crossed products (2000) Contemporary Math., 267, pp. 135-160
- Guccione, J.A., Guccione, J.J., Theory of braided Hopf crossed products (2003) Journal of Algebra, 261 (1), pp. 54-101
- Guccione, J.A., Guccione, J.J., Semiquasitriangular Hopf Algebras, , Preprint math QA/0302052
- Majid, S., Algebras and Hopf algebras in braided categories (1994) Advances in Hopf Algebras (Chicago IL 1992), 158, pp. 55-105. , Lecture Notes in Mathematics , Marcel Dekker
- Majid, S., (2000) Foundations of Quantum Group Theory, , Cambridge University Press
- Takeuchi, M., Survey of braided Hopf algebras (2000) Contemporary Math., 267, pp. 301-323
- Tambara, D., The endomorphism bialgebra of an algebra (1990) J. Fac. Sci. Univ. Tokyo Sect. IA, Math., 37, pp. 425-456
Citas:
---------- APA ----------
Di Luigi, C., Guccione, J.A. & Guccione, J.J. (2004) . Brzezinski's crossed products and braided Hopf crossed products. Communications in Algebra, 32(9), 3563-3580.http://dx.doi.org/10.1081/AGB-120039631
---------- CHICAGO ----------
Di Luigi, C., Guccione, J.A., Guccione, J.J. "Brzezinski's crossed products and braided Hopf crossed products" . Communications in Algebra 32, no. 9 (2004) : 3563-3580.http://dx.doi.org/10.1081/AGB-120039631
---------- MLA ----------
Di Luigi, C., Guccione, J.A., Guccione, J.J. "Brzezinski's crossed products and braided Hopf crossed products" . Communications in Algebra, vol. 32, no. 9, 2004, pp. 3563-3580.http://dx.doi.org/10.1081/AGB-120039631
---------- VANCOUVER ----------
Di Luigi, C., Guccione, J.A., Guccione, J.J. Brzezinski's crossed products and braided Hopf crossed products. Commun. Algebra. 2004;32(9):3563-3580.http://dx.doi.org/10.1081/AGB-120039631
