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Abstract:

We present a simple extension of the classical Hilton-Eckmann argument which proves that the endomorphism monoid of the unit object in a monoidal category is commutative. It allows us to recover in a uniform way well-known results on the graded-commutativity of cup products defined on the cohomology theories attached to various algebraic structures, as well as some more recent results.

Registro:

Documento: Artículo
Título:The Hilton-Heckmann argument for the anti-commutativity of cup products
Autor:Suarez-Alvarez, M.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Pabellón I, Buenos Aires (1428), Argentina
Año:2004
Volumen:132
Número:8
Página de inicio:2241
Página de fin:2246
DOI: http://dx.doi.org/10.1090/S0002-9939-04-07409-X
Handle:http://hdl.handle.net/20.500.12110/paper_00029939_v132_n8_p2241_SuarezAlvarez
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00029939_v132_n8_p2241_SuarezAlvarez.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v132_n8_p2241_SuarezAlvarez

Referencias:

  • Eckmann, B., Hilton, P.J., Group-like structures in general categories, I. Multiplications and comultiplications (1961) Math. Ann., 145, pp. 227-255. , MR 25:108
  • Gelfand, S.I., Manin, Y.I., Methods of homological algebra (2003) Springer Monographs in Mathematics, 2, pp. xx+372. , Springer-Verlag, Berlin. MR 2003m:18001
  • Gerstenhaber, M., The cohomology structure of an associative ring (1963) Ann. of Math. (2), 78, pp. 267-288. , MR 28:5102
  • Gerstenhaber, M., On the deformation of rings and algebras (1964) Ann. of Math. (2), 79, pp. 59-103. , MR 30:2034
  • Gerstenhaber, M., Schack, S.D., Bialgebra cohomology, deformations, and quantum groups (1990) Proc. Nat. Acad. Sci. U.S.A., 87 (1), pp. 478-481. , MR 90J:16062
  • Kassel, C., Quantum groups (1995) Graduate Texts in Mathematics, 155, pp. xii+531. , Springer-Verlag, New York. MR 96e:17041
  • Schauenburgi, P., Hopf modules and Yetter-Drinfel'd modules (1994) J. Algebra, 169 (3), pp. 874-890. , MR 95j:16047
  • Taillefer, R., Cohomology theories of Hopf bimodules and cup-product (2001) C. R. Acad. Sci. Paris Sér. I Math., 332 (3), pp. 189-194. , MR 2001m:16066
  • Taillefer, R., Injective Hopf Bimodules, Cohomologies of Infinite Dimensional Hopf Algebras and Graded-commutativity of the Yoneda Product

Citas:

---------- APA ----------
(2004) . The Hilton-Heckmann argument for the anti-commutativity of cup products. Proceedings of the American Mathematical Society, 132(8), 2241-2246.
http://dx.doi.org/10.1090/S0002-9939-04-07409-X
---------- CHICAGO ----------
Suarez-Alvarez, M. "The Hilton-Heckmann argument for the anti-commutativity of cup products" . Proceedings of the American Mathematical Society 132, no. 8 (2004) : 2241-2246.
http://dx.doi.org/10.1090/S0002-9939-04-07409-X
---------- MLA ----------
Suarez-Alvarez, M. "The Hilton-Heckmann argument for the anti-commutativity of cup products" . Proceedings of the American Mathematical Society, vol. 132, no. 8, 2004, pp. 2241-2246.
http://dx.doi.org/10.1090/S0002-9939-04-07409-X
---------- VANCOUVER ----------
Suarez-Alvarez, M. The Hilton-Heckmann argument for the anti-commutativity of cup products. Proc. Am. Math. Soc. 2004;132(8):2241-2246.
http://dx.doi.org/10.1090/S0002-9939-04-07409-X