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Abstract:

Let k be a characteristic zero field, C a k-algebra and M a square zero two sided ideal of C. We obtain a new mixed complex, simpler than the canonical one, giving the Hochschild and cyclic homologies of C relative to M. This complex resembles the canonical reduced mixed complex of an augmented algebra. We begin the study of our complex showing that it has a harmonic decomposition like to the one considered by Cuntz and Quillen for the normalized mixed complex of an algebra. We also give new proofs of two theorems of Goodwillie, obtaining a light improvement of one of them. © Walter de Gruyter 2006.

Registro:

Documento: Artículo
Título:Relative cyclic homology of square zero extensions
Autor:Guccione, J.A.; Guccione, J.J.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, (1428) Buenos Aires, Argentina
Año:2006
Número:600
Página de inicio:51
Página de fin:80
DOI: http://dx.doi.org/10.1515/CRELLE.2006.086
Título revista:Journal fur die Reine und Angewandte Mathematik
Título revista abreviado:J. Reine Angew. Math.
ISSN:00754102
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00754102_v_n600_p51_Guccione

Referencias:

  • Burghelea, D., Cyclic homology and algebraic K-theory of spaces I (1986) Contemp. Math., 55, pp. 89-115. , [B], Boulder, Colorado, 1983
  • Cortiñas, G., On the cyclic homology of commutative algebras over arbitrary ground rings (1999) Commun. Alg., 27 (3), pp. 1403-1412. , [Co]
  • Crainic, M., (2004) On the Perturbation Lemma, and Deformations, , [C], arXiv:Math. AT/0403266
  • Cuntz, J., Quillen, D., Operators on noncommutative differential forms and cyclic homology (1995) Geometry, Topology and Physics, pp. 77-111. , [C-Q], Raoul Bott International Press, Cambridge, MA
  • Gerstenhaber, M., Schack, S.D., Relative Hochschild cohomology, rigid algebras and the Bockstein (1986) J. Pure Appl. Alg., 43, pp. 53-74. , [G-S]
  • Goodwillie, T.G., Relative algebraic K-theory and cyclic homology (1986) Ann. Math., 124, pp. 347-402. , [G1]
  • Goodwillie, T.G., Cyclic homology, derivations and the free loop space (1985) Topology, 24, pp. 187-215. , [G2]
  • Kadison, L., (1984) Cyclic Homology of Extension Algebras with Application to Matrix Algebras, Algebraic K-theory, and Nest Algebras of Operators, , [K1], Ph. D. thesis, U. of Cal., Berkeley
  • Kadison, L., A relative cyclic cohomology theory useful for computations (1989) Cr. Acad. Sci. Paris, 308, pp. 569-573. , [K2]
  • Kassel, K., Cyclic homology, comodules and mixed complexes (1987) J. Alg., 107, pp. 195-216. , [Ka1]
  • Quillen, D., Cyclic cohomology and algebra extensions (1989) K-theory, 3, pp. 205-246. , [Q]

Citas:

---------- APA ----------
Guccione, J.A. & Guccione, J.J. (2006) . Relative cyclic homology of square zero extensions. Journal fur die Reine und Angewandte Mathematik(600), 51-80.
http://dx.doi.org/10.1515/CRELLE.2006.086
---------- CHICAGO ----------
Guccione, J.A., Guccione, J.J. "Relative cyclic homology of square zero extensions" . Journal fur die Reine und Angewandte Mathematik, no. 600 (2006) : 51-80.
http://dx.doi.org/10.1515/CRELLE.2006.086
---------- MLA ----------
Guccione, J.A., Guccione, J.J. "Relative cyclic homology of square zero extensions" . Journal fur die Reine und Angewandte Mathematik, no. 600, 2006, pp. 51-80.
http://dx.doi.org/10.1515/CRELLE.2006.086
---------- VANCOUVER ----------
Guccione, J.A., Guccione, J.J. Relative cyclic homology of square zero extensions. J. Reine Angew. Math. 2006(600):51-80.
http://dx.doi.org/10.1515/CRELLE.2006.086