Artículo
Abstract:
In this paper we present a direct proof of what is suggested by Holm's results (T. Holm, The Hochschild cohomology ring of a modular group algebra: the commutative case, Comm. Algebra 24, 1957-1969 (1996)): there is an isomorphism of algebras HH*(kG, kG) → kG ⊗ H*(G, k) where G is a finite abelian group, k a ring, HH*(kG, kG) is the Hochschild cohomology algebra and H*(G, k) the usual cohomology algebra. This result agrees with the well-known additive structure result in force for any group G; we remark that the multiplicative structure result we have obtained is quite similar to the description of the monoidal category of Hopf bimodules over kG given in "C. Cibils, Tensor product of Hopf bimodules, to appear in Proc. Amer. Math. Soc.". This similarity leads to conjecture the structure of HH*(kG, kG) for G a finite group.
Registro:
| Documento: | Artículo |
| Título: | Hochschild cohomology algebra of abelian groups |
| Autor: | Cibils, C.; Solotar, A. |
| Filiación: | Departement de Mathematiques, Université de Montpellier 2, Pl. Eugène Bataillon, F-34095 Montpellier Cedex 5, France Section de Mathématiques, Université de Genève, C.P. 240, CH-1211 Genève 24, Switzerland Dto. de Matemática, Fac. de Cs. Exactas y Nat., Ciudad Universitaria Pab.I, 1428 Buenos Aires, Argentina Mathématiques, Université de Paris XI, Bat. 425, F-91405 Orsay Cedex, France |
| Año: | 1997 |
| Volumen: | 68 |
| Número: | 1 |
| Página de inicio: | 17 |
| Página de fin: | 21 |
| DOI: | http://dx.doi.org/10.1007/PL00000389 |
| Título revista: | Archiv der Mathematik |
| Título revista abreviado: | Arch. Math. |
| ISSN: | 0003889X |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0003889X_v68_n1_p17_Cibils |
Referencias:
- Cyclic homology of algebras with one generator (1991) K-theory, 5, pp. 51-69
- Benson, D.J., (1991) Representations and Cohomology II: Cohomology of Groups and Modules, , Cambridge
- Cartan, H., Eilenberg, S., (1956) Homological Algebra, , Princeton, NJ
- Cibils, C., Tensor product of Hopf bimodules Proc. Amer. Math. Soc., , to appear
- Cibils, C., Rosso, M., Algèbres des chemins quantiques. Publication interne, genève 1993 et prépublication de l'IRMA 047 (1993) Adv. in Math., , Strasbourg to appear
- Cibils, C., Rosso, M., (1994) Hopf Bimodules Are Modules, , Preprint FIM-ETH Zurich
- Holm, T., The hochschild cohomology ring of a modular group algebra: The commutative case (1996) Comm. Algebra, 24, pp. 1957-1969
- Rosso, M., Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif (1978) Duke Math. J., 61, pp. 11-40
- Weibel, Ch., (1994) An Introduction to Homological Algebra, , Cambridge
- Woronowicz, S.L., Differential calculus on compact matrix pseudogroups (quantum groups) (1989) Commun. Math. Phys., 122, pp. 125-170
Citas:
---------- APA ----------
Cibils, C. & Solotar, A. (1997) . Hochschild cohomology algebra of abelian groups. Archiv der Mathematik, 68(1), 17-21.http://dx.doi.org/10.1007/PL00000389
---------- CHICAGO ----------
Cibils, C., Solotar, A. "Hochschild cohomology algebra of abelian groups" . Archiv der Mathematik 68, no. 1 (1997) : 17-21.http://dx.doi.org/10.1007/PL00000389
---------- MLA ----------
Cibils, C., Solotar, A. "Hochschild cohomology algebra of abelian groups" . Archiv der Mathematik, vol. 68, no. 1, 1997, pp. 17-21.http://dx.doi.org/10.1007/PL00000389
---------- VANCOUVER ----------
Cibils, C., Solotar, A. Hochschild cohomology algebra of abelian groups. Arch. Math. 1997;68(1):17-21.http://dx.doi.org/10.1007/PL00000389
