Abstract:
We define a type of crossed product over braided Hopf algebras, which generalizes the ones introduced by Blattner, Cohen, and Montgomery, and Doi and Takeuchi, and we study some of its properties. For instance, we prove Maschke's Theorem for these new crossed products and we construct a natural Morita context which extends the one obtained by Cohen, Fischman, and Montgomery. © 2003 Elsevier Science (USA). All rights reserved.
Referencias:
- Alonso Alvarez, J.N., Fernádez Vilaboa, J.M., Cleft extensions in braided categories (2000) Comm. Algebra, 28 (7), pp. 3185-3196
- Andruskiewitsch, N., Graña, M., Braided Hopf algebras over non-abelian finite groups (1999) Bol. Acad. Nac. Cienc. De Cordoba (Argentina), 63, pp. 45-78
- Andruskiewitsch, N., Schneider, H.J., Lifting of quantum linear spaces and pointed Hopf algebras of order p3 (1998) J. Algebra, 209, pp. 659-691
- Bespalov, Y., Crossed modules and quantum groups in braided categories (1997) Appl. Categ. Structures, 5, pp. 155-204
- Bespalov, Y., Drabant, B., Cross products bialgebras , (PART II). , math.QA/9904142; Blattner, R.J., Cohen, M., Montgomery, S., Crossed products and inner actions of Hopf algebras (1986) Trans. Amer. Math. Soc., 298, pp. 671-711
- Blattner, R.J., Montgomery, S., Crossed products and Galois extensions of Hopf algebras (1989) Pacific J. Math., 137, pp. 37-54
- Brzeziński, T., Crossed products by a coalgebra (1997) Comm. Algebra, 25, pp. 3551-3575
- Cohen, M., Fischman, D., Hopf algebra actions (1986) J. Algebra, 100, pp. 363-379
- 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
- Dǎscǎlescu, S., Nǎstǎsescu, C., Raianu, S., Hopf Algebras. An Introduction (2001) Pure Appl. Math., 235. , Dekker, New York
- Doi, Y., Hopf comodules in Yetter-Drinfeld categories (1998) Comm. Algebra, 26, pp. 3057-3070
- Doi, Y., Equivalent crossed products for a Hopf algebra (1989) Comm. Algebra, 17, pp. 3053-3085
- Doi, Y., Takeuchi, M., Cleft comodule algebras by a bialgebra (1986) Comm. Algebra, 14, pp. 801-817
- Fichman, 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., A generalization of crossed products (2000) Contemp. Math., 267, pp. 135-160
- Larson, R., Sweedler, M.E., An associative orthogonal bilinear form for Hopf algebras (1969) Amer. J . Math., 91, pp. 75-94
- Lyuvashenko, V., Hopf algebras and vector symmetries (1988) Russian Math. Surveys, 4, pp. 153-154
- Lyuvashenko, V., Modular transformations for tensor categories (1995) J. Pure Appl. Algebra, 98, pp. 279-327
- Majid, S., Crossed products by braided groups and bosonization (1994) J. Algebra, 163, pp. 165-190
- Montgomery, S., Hopf Algebras and Their Actions on Rings (1993) CBMS Regional Conf. Ser. Math., 82. , Amer. Math. Society, Providence, RI
- Schauenburg, P., A generalization of crossed products Preprint; 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
- Tambara, D., The endomorphism bialgebra of an algebra (1990) J. Fac. Sci. Univ. Tokyo Sect. IA, 37, pp. 425-456
Citas:
---------- APA ----------
Guccione, J.A. & Guccione, J.J.
(2003)
. Theory of braided Hopf crossed products. Journal of Algebra, 261(1), 54-101.
http://dx.doi.org/10.1016/S0021-8693(02)00546-X---------- CHICAGO ----------
Guccione, J.A., Guccione, J.J.
"Theory of braided Hopf crossed products"
. Journal of Algebra 261, no. 1
(2003) : 54-101.
http://dx.doi.org/10.1016/S0021-8693(02)00546-X---------- MLA ----------
Guccione, J.A., Guccione, J.J.
"Theory of braided Hopf crossed products"
. Journal of Algebra, vol. 261, no. 1, 2003, pp. 54-101.
http://dx.doi.org/10.1016/S0021-8693(02)00546-X---------- VANCOUVER ----------
Guccione, J.A., Guccione, J.J. Theory of braided Hopf crossed products. J. Algebra. 2003;261(1):54-101.
http://dx.doi.org/10.1016/S0021-8693(02)00546-X