Artículo
Herscovich, E.; Solotar, A. "Derived invariance of Hochschild-Mitchell (co)homology and one-point extensions" (2007) Journal of Algebra. 315(2):852-873
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Abstract:
In this article we prove derived invariance of Hochschild-Mitchell homology and cohomology and we extend to k-linear categories a result by Barot and Lenzing concerning derived equivalences and one-point extensions. We also prove the existence of a long exact sequence à la Happel and we give a generalization of this result which provides an alternative approach. © 2007 Elsevier Inc. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | Derived invariance of Hochschild-Mitchell (co)homology and one-point extensions |
| Autor: | Herscovich, E.; Solotar, A. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon 1, 1428 Buenos Aires, Argentina |
| Palabras clave: | Derived equivalence; Hochschild-Mitchell cohomology; k-Category; One-point extension |
| Año: | 2007 |
| Volumen: | 315 |
| Número: | 2 |
| Página de inicio: | 852 |
| Página de fin: | 873 |
| DOI: | http://dx.doi.org/10.1016/j.jalgebra.2007.05.014 |
| Título revista: | Journal of Algebra |
| Título revista abreviado: | J. Algebra |
| ISSN: | 00218693 |
| CODEN: | JALGA |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00218693_v315_n2_p852_Herscovich.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v315_n2_p852_Herscovich |
Referencias:
- Anderson, F., Fuller, K., Rings and Categories of Modules (1992) Grad. Texts in Math. second ed., 13. , Springer-Verlag, New York
- Barot, M., Lenzing, H., One-point extensions and derived equivalence (2003) J. Algebra, 264 (1), pp. 1-5
- Cibils, C., Tensor Hochschild homology and cohomology (2000) Lect. Notes Pure Appl. Math., 210, pp. 35-51. , Interactions Between Ring Theory and Representations of Algebras, Murcia, Dekker, New York
- Cibils, C., Marcos, E., Skew category, Galois covering and smash product of a category over a ring (2006) Proc. Amer. Math. Soc., 134 (1), pp. 39-50
- Cibils, C., Redondo, M.J., Cartan-Leray spectral sequence for Galois coverings of categories (2005) J. Algebra, 284 (1), pp. 310-325
- Cibils, C., Solotar, A., Galois coverings, Morita equivalences and smash extensions of categories over a field (2006) Doc. Math., 11, pp. 143-159
- Green, E., Marcos, E., Snashall, N., The Hochschild cohomology ring of a one point extension (2003) Comm. Algebra, 31 (1), pp. 357-379
- Green, E., Solberg, Ø., Hochschild cohomology rings and triangular rings (2002) Representations of Algebras, vols. I, II, pp. 192-200. , Beijing Normal Univ. Press, Beijing
- Happel, D., Hochschild cohomology of finite-dimensional algebras (1989) Lecture Notes in Math., 1404, pp. 108-126. , Séminaire d'Algèbre Paul Dubreil et Marie-Paul Malliavin, 39ème Année. Paris, 1987/1988, Springer-Verlag, Berlin
- Herscovich, E., Solotar, A., Hochschild-Mitchell cohomology and Galois extensions (2006) J. Pure Appl. Algebra, 209 (1), pp. 37-55. , (online since July 11th) math.KT/0510160
- Keller, B., Deriving DG categories (1994) Ann. Sci. École Norm. Sup. (4), 27 (1), pp. 63-102
- Krause, H., Derived categories, resolutions, and Brown representability, , Summer School Chicago 2004, pp. 1-30. math.KT/0511047
- Michelena, S., Platzeck, M., Hochschild cohomology of triangular matrix algebras (2000) J. Algebra, 233 (2), pp. 502-525
- Mitchell, B., Rings with several objects (1972) Adv. Math., 8, pp. 1-161
Citas:
---------- APA ----------
Herscovich, E. & Solotar, A. (2007) . Derived invariance of Hochschild-Mitchell (co)homology and one-point extensions. Journal of Algebra, 315(2), 852-873.http://dx.doi.org/10.1016/j.jalgebra.2007.05.014
---------- CHICAGO ----------
Herscovich, E., Solotar, A. "Derived invariance of Hochschild-Mitchell (co)homology and one-point extensions" . Journal of Algebra 315, no. 2 (2007) : 852-873.http://dx.doi.org/10.1016/j.jalgebra.2007.05.014
---------- MLA ----------
Herscovich, E., Solotar, A. "Derived invariance of Hochschild-Mitchell (co)homology and one-point extensions" . Journal of Algebra, vol. 315, no. 2, 2007, pp. 852-873.http://dx.doi.org/10.1016/j.jalgebra.2007.05.014
---------- VANCOUVER ----------
Herscovich, E., Solotar, A. Derived invariance of Hochschild-Mitchell (co)homology and one-point extensions. J. Algebra. 2007;315(2):852-873.http://dx.doi.org/10.1016/j.jalgebra.2007.05.014
