Artículo
Cibils, C.; Solotar, A. "Galois coverings, morita equivalence and smash extensions of categories over a field" (2006) Documenta Mathematica. 11(1):143-159
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Abstract:
Algebras over a field k generalize to categories over k in order to considers Galois coverings. Two theories presenting analogies, namely smash extensions and Galois coverings with respect to a finite group are known to be different. However we prove in this paper that they are Morita equivalent. For this purpose we need to describe explicit processes providing Morita equivalences of categories which we call contraction and expansion. A structure theorem is obtained: composition of these processes provides any Morita equivalence up to equivalence, a result which is related with the karoubianisation (or idempotent completion) and additivisation of a k-category.
Registro:
| Documento: | Artículo |
| Título: | Galois coverings, morita equivalence and smash extensions of categories over a field |
| Autor: | Cibils, C.; Solotar, A. |
| Filiación: | Département de Mathématiques, Université de Montpellier 2, F-34095 Montpellier cedex 5, France Departemento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón 1, 1428, Buenos Aires, Argentina |
| Palabras clave: | Completion; Galois covering; Hopf algebra; K-category; Karoubianisation; Morita theory; Smash product |
| Año: | 2006 |
| Volumen: | 11 |
| Número: | 1 |
| Página de inicio: | 143 |
| Página de fin: | 159 |
| Título revista: | Documenta Mathematica |
| Título revista abreviado: | Doc. Math. |
| ISSN: | 14310635 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v11_n1_p143_Cibils |
Referencias:
- Balmer, P., Schlichting, M., Idempotent completion of triangulated categories (2001) J. Algebra, 236, pp. 819-834
- Beattie, M., Torrecillas, B., Twistings and Hopf Galois extensions (2000) J. Algebra, 232, pp. 673-696
- Bongartz, K., Gabriel, P., Covering spaces in representation-theory (1981) Invent. Math., 65, pp. 331-378
- Cibils, C., Marcos, E.N., Skew categories, Galois coverings and smash product of a k-category (2006) Proc. Amer. Math. Soc., 134, pp. 39-50
- Cibils, C., Redondo, M.J., Cartan-Leray spectral sequence for Galois coverings of linear categories (2005) J. Algebra, 284, pp. 310-325
- Cohen, M., Montgomery, S., Group-graded rings, smash products, and group actions (1984) Trans. Amer. Math. Soc., 282, pp. 237-258
- Drozd, Y.A., Ovsienko, S.A., Coverings of Tame Boxes and Algebras, , Preprints of the Max-Planck-Institut für Mathematik. MPI 2000 - 26
- Freyd, P., Abelian categories. An introduction to the theory of functors (1964) Harper's Series in Modern Mathematics, , http://www.tac.mta.ca/tac/reprints/articles/3/tr3.pdf, New York-Evanston-London: Harper and Row, Publishers
- Gabriel, P., The universal cover of a representation-finite algebra (1981) Lecture Notes in Math., 903, pp. 68-105. , Representations of algebras Puebla, 1980 , Springer, Berlin-New York
- Green, E.L., Graphs with relations, coverings, and group-graded algebras (1983) Trans. Amer. Math. Soc., 279, pp. 297-310
- Kreimer, H.F., Normal bases for Hopf-Galois algebras (2002) Proc. Amer. Math. Soc., 130, pp. 2853-2856
- Lorenz, M., On the homology of graded algebras (1992) Comm. Algebra, 20, pp. 489-507
- Mitchell, B., Rings with several objects (1972) Adv. in Math., 8, pp. 1-161
- Mitchell, B., Separable algebroids (1985) AMS Memoirs, 333
- Montgomery, S., Hopf algebras and their actions on rings (1993) CBMS Regional Conference Series in Mathematics, 82. , Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI
- Redondo, M.-J., Pirashvili, T., Cohomology of the Grothendieck Construction, , http://arxiv.org/abs/math/0504282
- Raianu, Ş., Saorín, M., Finite Hopf-Galois extensions equivalent to crossed products (2001) Comm. Algebra, 29, pp. 4871-4882
- Tillmann, U., S-structures for k-linear categories and the definition of a modular functor (1998) J. Lond. Math. Soc. II, 58, pp. 208-228
- Weibel, C., An introduction to homological algebra (1994) Cambridge Studies in Advanced Mathematics, 38. , Cambridge: Cambridge University Press
Citas:
---------- APA ----------
Cibils, C. & Solotar, A. (2006) . Galois coverings, morita equivalence and smash extensions of categories over a field. Documenta Mathematica, 11(1), 143-159.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v11_n1_p143_Cibils [ ]
---------- CHICAGO ----------
Cibils, C., Solotar, A. "Galois coverings, morita equivalence and smash extensions of categories over a field" . Documenta Mathematica 11, no. 1 (2006) : 143-159.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v11_n1_p143_Cibils [ ]
---------- MLA ----------
Cibils, C., Solotar, A. "Galois coverings, morita equivalence and smash extensions of categories over a field" . Documenta Mathematica, vol. 11, no. 1, 2006, pp. 143-159.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v11_n1_p143_Cibils [ ]
---------- VANCOUVER ----------
Cibils, C., Solotar, A. Galois coverings, morita equivalence and smash extensions of categories over a field. Doc. Math. 2006;11(1):143-159.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14310635_v11_n1_p143_Cibils [ ]
