Navegar

Colección

Datos Estadísticas

Artículo

Este artículo es de Acceso Abierto y puede ser descargado en su versión final desde nuestro repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

Let k be a field, A a unitary associative k-algebra and V a k-vector space endowed with a distinguished element 1V. We obtain a mixed complex, simpler than the canonical one, that gives the Hochschild, cyclic, negative and periodic homologies of a crossed product E := A #fV, in the sense of Brzeziński. We actually work in the more general context of relative cyclic homology. Specifically, we consider a subalgebra K of A that satisfies suitable hypothesis and we find a mixed complex computing the Hochschild, cyclic, negative and periodic homologies of E relative to K. Then, when E is a cleft braided Hopf crossed product, we obtain a simpler mixed complex, that also gives the Hochschild, cyclic, negative and periodic homologies of E. © 2012 Elsevier Ltd.

Registro:

Documento: Artículo
Título:Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products
Autor:Carboni, G.; Guccione, J.A.; Guccione, J.J.; Valqui, C.
Filiación:Cíclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria-Pabellón3, (C1428EGA) Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria-Pabellón1, (C1428EGA) Buenos Aires, Argentina
Pontificia Universidad Católica del Perú, Instituto de Matemática y Ciencias Afines, Sección Matemáticas, PUCP, Av. Universitaria 1801, San Miguel, Lima 32, Peru
Palabras clave:Crossed products; Cyclic homology; Hochschild (co)homology
Año:2012
Volumen:231
Número:6
Página de inicio:3502
Página de fin:3568
DOI: http://dx.doi.org/10.1016/j.aim.2012.09.006
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00018708_v231_n6_p3502_Carboni.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v231_n6_p3502_Carboni

Referencias:

  • Akbarpour, R., Khalkhali, M., Hopf algebra equivariant cyclic homology and cyclic homology of crossed product algebras (2003) J. Reine Angew. Math., 559, pp. 137-152
  • Bespalov, Y., Drabant, B., Cross products bialgebras, Part II (2001) J. Algebra, 240, pp. 445-504
  • Blattner, R.J., Cohen, M., Montgomery, S., Crossed products and inner actions of Hopf algebras (1986) Trans. Amer. Math. Soc., 298, pp. 671-711
  • Bonneau, P., Gerstenhaber, M., Giaquinto, A., Sternheimer, D., Quantum groups and deformation quantization: explicit approaches and implicit aspects (2004) J. Math. Phys., 45, pp. 3703-3741
  • Bonneau, P., Sternheimer, D., Topological Hopf algebras, quantum groups and deformation quantization (2005) Lect. Notes Pure Appl. Math., 239, pp. 55-70
  • Burghelea, D., Cyclic homology and algebraic K-theory of spaces I (1986) Contemp. Math., 55, pp. 89-115. , Boulder Colorado 1983
  • Brzeziński, T., Crossed products by a coalgebra (1997) Comm. Algebra, 25, pp. 3551-3575
  • Carboni, G., Guccione, J.A., Guccione, J.J., Cyclic homology of crossed products (2010) Adv. Math., 223, pp. 840-872
  • Crainic, M., (2004), On the perturbation lemma, and deformations, arxiv:Math.AT/0403266; Doi, Y., Takeuchi, M., Cleft comodule algebras by a bialgebra (1986) Comm. Algebra, 14, pp. 801-817
  • Feigin, B.L., Tsygan, B.L., Additive K-Theory, K-Theory, Arithmetic and Geometry, (Moscow, 1984-1986) (1987) Lecture Notes in Mathematics, 1289, pp. 67-209. , Springer, Berlin
  • Guccione, J.A., Guccione, J.J., Hochschild homology of twisted tensor products (1999) K-Theory, 18, pp. 363-400
  • Guccione, J.A., Guccione, J.J., Theory of braided Hopf crossed products (2003) J. Algebra, 261 (1), pp. 54-101
  • Guccione, J.A., Guccione, J.J., Hochschild (co)homology of Hopf crossed products (2002) K-Theory, 25, pp. 138-169
  • Getzler, E., Jones, J.D., The cyclic homology of crossed product algebras (1993) J. Reine Angew. Math., 445, pp. 161-174
  • Gerstenhaber, M., Schack, S.D., Relative Hochschild cohomology, rigid algebras and the Bockstein (1986) J. Pure Appl. Algebra, 43, pp. 53-74
  • Hochschild, G., Serre, J.P., Cohomology of group extensions (1953) Trans. Amer. Math. Soc., 74, pp. 110-134
  • Jara, P., Stefan, D., Hopf cyclic homology and relative cyclic homology of Hopf Galois extensions (2006) Proc. Lond. Math. Soc., 93 (3), pp. 138-174
  • Kassel, C., Cyclic homology, comodules and mixed complexes (1987) J. Algebra, 107, pp. 195-216
  • Khalkhali, M., Rangipour, B., On the cyclic homology of Hopf crossed products (2004) Fields Inst. Commun., 43, pp. 341-351
  • Majid, S., Algebras and Hopf Algebras in Braided Categories (1994) Marcel Dekker L. N. in Math., 158, pp. 55-105
  • Nistor, V., Group cohomology and the cyclic cohomology of crossed products (1990) Invent. Math., 99, pp. 411-424
  • Takeuchi, M., Survey of braided Hopf algebras (2000) Contemp. Math., 267, pp. 301-323
  • Zang, J., Hu, N., Cyclic homology of strong smash product algebras (2012) J. Reine Angew. Math., 663, pp. 177-207

Citas:

---------- APA ----------
Carboni, G., Guccione, J.A., Guccione, J.J. & Valqui, C. (2012) . Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products. Advances in Mathematics, 231(6), 3502-3568.
http://dx.doi.org/10.1016/j.aim.2012.09.006
---------- CHICAGO ----------
Carboni, G., Guccione, J.A., Guccione, J.J., Valqui, C. "Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products" . Advances in Mathematics 231, no. 6 (2012) : 3502-3568.
http://dx.doi.org/10.1016/j.aim.2012.09.006
---------- MLA ----------
Carboni, G., Guccione, J.A., Guccione, J.J., Valqui, C. "Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products" . Advances in Mathematics, vol. 231, no. 6, 2012, pp. 3502-3568.
http://dx.doi.org/10.1016/j.aim.2012.09.006
---------- VANCOUVER ----------
Carboni, G., Guccione, J.A., Guccione, J.J., Valqui, C. Cyclic homology of Brzeziński's crossed products and of braided Hopf crossed products. Adv. Math. 2012;231(6):3502-3568.
http://dx.doi.org/10.1016/j.aim.2012.09.006