Abstract:
Let k be a field and let H be a rigid braided Hopf k-algebra. In this paper we continue the study of the theory of braided Hopf crossed products began in [J.A. Guccione, J.J. Guccione, Theory of braided Hopf crossed products, J. Algebra 261 (2003) 54-101]. First we show that to have an H-braided comodule algebra is the same that to have an H†-braided module algebra, where H† is a variant of H*, and then we study the maps [,] and (,), that appear in the Morita context introduced in the above cited paper. © 2006.
Registro:
Documento: |
Artículo
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Título: | Braided module and comodule algebras, Galois extensions and elements of trace 1 |
Autor: | Da Rocha, M.; Guccione, J.A.; Guccione, J.J. |
Filiación: | Cíclo Básico Común, Pabellón 3, (1428) Buenos Aires, Argentina Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Pabellón 1, (1428) Buenos Aires, Argentina
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Palabras clave: | Braided Hopf algebras; Crossed products; Galois extensions |
Año: | 2007
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Volumen: | 307
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Número: | 2
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Página de inicio: | 727
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Página de fin: | 768
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DOI: |
http://dx.doi.org/10.1016/j.jalgebra.2006.05.008 |
Título revista: | Journal of Algebra
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Título revista abreviado: | J. Algebra
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ISSN: | 00218693
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CODEN: | JALGA
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PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00218693_v307_n2_p727_DaRocha.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v307_n2_p727_DaRocha |
Referencias:
- Andruskiewitsch, N., Graña, M., Braided Hopf algebras over non-abelian finite groups (1999) Bol. Acad. Nac. Cienc. (Córdoba), 63, pp. 45-78
- Andruskiewitsch, N., Schneider, H.J., Hopf algebras of order p2 and braided Hopf algebras of order p (1998) J. Algebra, 199, pp. 430-454
- Bespalov, Y., Kerler, T., Lyubashenko, V., Turaev, V., Integrals for braided Hopf algebras (2000) J. Pure Appl. Algebra, 148 (2), pp. 113-164
- Cohen, M., Fischman, D., Semisimple extensions and elements of trace 1 (1992) J. Algebra, 149, pp. 419-437
- Cohen, M., Fischman, D., Montgomery, S., Hopf Galois extensions, smash products and Morita equivalence (1990) J. Algebra, 133, pp. 351-372
- Cap, A., Schichl, H., Vanzura, J., On twisted tensor products of algebras (1995) Comm. Algebra, 23, pp. 4701-4735
- Doi, Y., Hopf modules in Yetter-Drinfeld categories (1998) Comm. Algebra, 26, pp. 3057-3070
- Di Luigi, C., Guccione, J.A., Guccione, J.J., Brzeziński's crossed products and braided Hopf crossed products (2004) Comm. Algebra, 32, pp. 3563-3580
- Faith, C., (1973) Ring, Modules and Categories, , Springer-Verlag, Berlin
- Fischman, D., Montgomery, S., Schneider, H.J., Frobenius extensions of subalgebras of Hopf algebras (1997) Trans. Amer. Math. Soc., 349, pp. 4857-4895
- Guccione, J.A., Guccione, J.J., Theory of braided Hopf crossed products (2003) J. Algebra, 261, pp. 54-101
- Hirata, K., Sugano, K., On semi-simple and separable extensions over non-commutative rings (1966) J. Math. Soc. Japan, 18 (4), pp. 360-373
- Kreimer, H.F., Takeuchi, M., Hopf algebras and Galois extensions of an algebra (1981) Indiana Math. J., 30, pp. 675-692
- Lyubashenko, V., Modular transformations for tensor categories (1995) J. Pure Appl. Algebra, 98, pp. 279-327
- Lyubashenko, V., Hopf algebras and vector symmetries (1988) Russian Math. Surveys, 4, pp. 153-154
- Montgomery, S., Hopf Algebras and Their Actions on Rings (1993) CBMS Reg. Conf. Ser. Math., 82. , Amer. Math. Soc., Providence, RI
- Schneider, H.J., Normal basis and transitivity of crossed products for Hopf algebras (1992) J. Algebra, 152, pp. 289-312
- Takeuchi, M., Survey of braided Hopf algebras (2000) Contemp. Math., 267, pp. 301-323
- Takeuchi, M., Finite Hopf algebras in braided tensor categories (1999) J. Pure Appl. Algebra, 138, pp. 59-82
Citas:
---------- APA ----------
Da Rocha, M., Guccione, J.A. & Guccione, J.J.
(2007)
. Braided module and comodule algebras, Galois extensions and elements of trace 1. Journal of Algebra, 307(2), 727-768.
http://dx.doi.org/10.1016/j.jalgebra.2006.05.008---------- CHICAGO ----------
Da Rocha, M., Guccione, J.A., Guccione, J.J.
"Braided module and comodule algebras, Galois extensions and elements of trace 1"
. Journal of Algebra 307, no. 2
(2007) : 727-768.
http://dx.doi.org/10.1016/j.jalgebra.2006.05.008---------- MLA ----------
Da Rocha, M., Guccione, J.A., Guccione, J.J.
"Braided module and comodule algebras, Galois extensions and elements of trace 1"
. Journal of Algebra, vol. 307, no. 2, 2007, pp. 727-768.
http://dx.doi.org/10.1016/j.jalgebra.2006.05.008---------- VANCOUVER ----------
Da Rocha, M., Guccione, J.A., Guccione, J.J. Braided module and comodule algebras, Galois extensions and elements of trace 1. J. Algebra. 2007;307(2):727-768.
http://dx.doi.org/10.1016/j.jalgebra.2006.05.008