Artículo
Farinati, M.A. "On the Derived Invariance of Cohomology Theories for Coalgebras" (2003) Algebras and Representation Theory. 6(3):303-331
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Abstract:
We study the derived invariance of the cohomology theories Hoch*, H* and HC* associated with coalgebras over a field. We prove a theorem characterizing derived equivalences. As particular cases, it describes the two following situations: (1) f: C → D a quasi-isomorphism of differential graded coalgebras, (2) the existence of a 'cotilting' bicomodule CTD In these two cases we construct a derived-Morita equivalence context, and consequently we obtain isomorphisms Hoch*(C) ≅ Hoch*(D) and H*(C) ≅ H*(D). Moreover, when we have a coassociative map inducing an isomorphism H*(C) ≅ H* (D) (for example, when there is a quasi-isomorphism f: C → D), we prove that HC*(C) ≅ HC*(D).
Registro:
| Documento: | Artículo |
| Título: | On the Derived Invariance of Cohomology Theories for Coalgebras |
| Autor: | Farinati, M.A. |
| Filiación: | Dto. de Matemática FCEyN, Uniyersidad de Buenos Aires, Cdad. Universitaria Pab I. (1428), Buenos Aires, Argentina |
| Palabras clave: | Coalgebras; Derived categories; Hochschild homology; Geometry; Problem solving; Theorem proving; Derived categories; Algebra |
| Año: | 2003 |
| Volumen: | 6 |
| Número: | 3 |
| Página de inicio: | 303 |
| Página de fin: | 331 |
| DOI: | http://dx.doi.org/10.1023/A:1025114311299 |
| Título revista: | Algebras and Representation Theory |
| Título revista abreviado: | Algebr Represent Theory |
| ISSN: | 1386923X |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1386923X_v6_n3_p303_Farinati |
Referencias:
- Doi, Y., Homological coalgebra (1981) J. Math. Soc. Japan., 33 (1), pp. 31-50
- Hartshorne, R., Residues and Duality (1966) Lecture Notes in Math., 20. , Springer, New York
- Farinati, M.A., (1999) Teorías de Cohomología de Coálgebras, , PhD thesis, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires
- Farinati, M.A., Solotar, A.L., Morita-Takeuchi equivalence, cohomology of coalgebras and Azumaya coalgebras (1998) Lecture Notes in Pure and Appl. Math., 197. , Rings, Hopf Algebras, and Brauer Groups, Marcel Dekker, New York
- Farinati, M.A., Solotar, A.L., Cyclic homology of coalgebras Lecture Notes in Pure and Appl. Math., , Hopf Algebras and Quantum Groups, Marcel Dekker, New York
- Keller, B., Tilting theory and differential graded algebras (1994) Proc. Nato ARW on Representation of Algebras and Related Topics, , V. Dlab and L. Scott (eds), Kluwer Acad. Publ., Dordrecht
- Gelfand, S.I., Manin, Y.I., (1996) Methods of Homological Algebra, , Springer, New York
- Takeuchi, M., Monta theorems for categories of comodules (1977) J. Fac. Sci. Univ. Tokyo, 24, pp. 1483-1528
Citas:
---------- APA ----------
(2003) . On the Derived Invariance of Cohomology Theories for Coalgebras. Algebras and Representation Theory, 6(3), 303-331.http://dx.doi.org/10.1023/A:1025114311299
---------- CHICAGO ----------
Farinati, M.A. "On the Derived Invariance of Cohomology Theories for Coalgebras" . Algebras and Representation Theory 6, no. 3 (2003) : 303-331.http://dx.doi.org/10.1023/A:1025114311299
---------- MLA ----------
Farinati, M.A. "On the Derived Invariance of Cohomology Theories for Coalgebras" . Algebras and Representation Theory, vol. 6, no. 3, 2003, pp. 303-331.http://dx.doi.org/10.1023/A:1025114311299
---------- VANCOUVER ----------
Farinati, M.A. On the Derived Invariance of Cohomology Theories for Coalgebras. Algebr Represent Theory. 2003;6(3):303-331.http://dx.doi.org/10.1023/A:1025114311299
