From topological homology: algebras with different properties of homological triviality

  • A. Ya. Helemskii
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1520)


Banach Algebra Cohomology Group Left Inverse Commutative Banach Algebra Cyclic Cohomology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Putinar M. On analytic modules: softness and quasicoherence. Complex analysis and applications, 1985, Publ. House of the Bulgarian Acad. Sci. Sofia, 1986, 534–547.Google Scholar
  2. 2.
    Connes A. Non-commutative differential geometry, Parts I and II, I.H.E.S. 62 (1985), 157–360.Google Scholar
  3. 3.
    Tzygan B.L. Homology of matrix Lie algebras over rings and Hochschild homology, Uspekhi Mat. Nauk 38 (1983), 217–218 (in Russian).MathSciNetGoogle Scholar
  4. 4.
    Christensen E., Sinclair A.M. On the vanishing of Hn(A,A*) for certain C*-algebras, Pacific J. Math. 137 (1989), 55–63.MathSciNetCrossRefzbMATHGoogle Scholar
  5. B.
    Helemskii A.Ya. The Homology of Banach and Topological Algebras. Kluwer, Dordrecht, 1989.CrossRefGoogle Scholar
  6. 5.
    Helemskii A.Ya. Banach and polynormed algebras: the general theory, representations, homology. Nauka, Moscow, 1989 (in Russian) — to be translated into English, Oxford Univ. Press, London, 1991.Google Scholar
  7. 6.
    Operator algebras and applications. Proc. of Symp. in Pure Math., v.38, Part II. Kadison R.V., ed. Providence, 1982.Google Scholar
  8. 7.
    Christensen E., Evans D.E. Cohomology of operator algebras and quantum dynamical semigroups, J. London Math. Soc. 20 (1979).Google Scholar
  9. 8.
    Effros E.G. Advances in quantized functional analysis. Proc. ICM, 1986, v.2, 906–916.MathSciNetGoogle Scholar
  10. 9.
    Helemskii A. Ya. Homological algebra background of the "amenability-after-Connes":injectivity of the predual bimodule, Mat. Sb. 180, no.12, 1680–1690 (in Russian).Google Scholar
  11. 10.
    Christensen E., Effros E.G., Sinclair A.M. Completely bounded multilinear maps and C*-algebraic cohomology, Invent. Math. 90 (1987), 279–296.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 11.
    Bade W.G., Curtis P.C., Dales H.G. Amenability and weak amenability for Beurling and Lipshitz algebras, Proc. London Math. Soc. (3) 55 (1987), 359–377.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 12.
    Groenbaek N. A characterization of weakly amenable algebras, Studia Math. XCIV (1989) 149–162.MathSciNetzbMATHGoogle Scholar
  14. 13.
    Connes A. Cohomologie cyclique et foncteur Extn, C.R.Acad. Sci. Paris, serie I, 296 (1983), 953–958.MathSciNetzbMATHGoogle Scholar
  15. 14.
    Pugach L.I. Homological properties of functional algebras and analytic polydiscs in their maximal ideal spaces, Rev. Roumaine Math. Pure and Appl. 31 (1986), 347–356 (in Russian).MathSciNetzbMATHGoogle Scholar
  16. 15.
    Ogneva O.S. Coincidence of homological dimensions of Frechet algebra of smooth functions on a manifold with the dimension of the manifold, Funct. anal. i pril. 20 (1986), 92–93 (in Russian).MathSciNetzbMATHGoogle Scholar
  17. 16.
    Golovin Yu.O. Homological properties of Hilbert modules over nest operator algebras, Mat. Zametki 41 (1987), 769–775 (in Russian).MathSciNetzbMATHGoogle Scholar
  18. 17.
    Effros E.G. Amenability and virtual diagonals for von Neumann algebras, J. Funct. Anal. v.78 (1988), 137–153.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 18.
    Lazar A.J., Tsui S.-K., Wright S. A cohomological characterization of finite-dimensional C*-algebras, J. Operator Theory 14 (1985)Google Scholar
  20. 19.
    Choi M.-D., Effros E.G. Nuclear C*-algebras and injectivity: the general case, Indiana Univ. Math. J. 26(1977), 443–446.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • A. Ya. Helemskii
    • 1
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowUSSR

Personalised recommendations