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From topological homology: algebras with different properties of homological triviality

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1520)

Keywords

  • Banach Algebra
  • Cohomology Group
  • Left Inverse
  • Commutative Banach Algebra
  • Cyclic Cohomology

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References

  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. Connes A. Non-commutative differential geometry, Parts I and II, I.H.E.S. 62 (1985), 157–360.

    Google Scholar 

  3. Tzygan B.L. Homology of matrix Lie algebras over rings and Hochschild homology, Uspekhi Mat. Nauk 38 (1983), 217–218 (in Russian).

    MathSciNet  Google Scholar 

  4. Christensen E., Sinclair A.M. On the vanishing of Hn(A,A*) for certain C*-algebras, Pacific J. Math. 137 (1989), 55–63.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Helemskii A.Ya. The Homology of Banach and Topological Algebras. Kluwer, Dordrecht, 1989.

    CrossRef  Google Scholar 

  6. 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. Operator algebras and applications. Proc. of Symp. in Pure Math., v.38, Part II. Kadison R.V., ed. Providence, 1982.

    Google Scholar 

  8. Christensen E., Evans D.E. Cohomology of operator algebras and quantum dynamical semigroups, J. London Math. Soc. 20 (1979).

    Google Scholar 

  9. Effros E.G. Advances in quantized functional analysis. Proc. ICM, 1986, v.2, 906–916.

    MathSciNet  Google Scholar 

  10. 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. Christensen E., Effros E.G., Sinclair A.M. Completely bounded multilinear maps and C*-algebraic cohomology, Invent. Math. 90 (1987), 279–296.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. 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.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Groenbaek N. A characterization of weakly amenable algebras, Studia Math. XCIV (1989) 149–162.

    MathSciNet  MATH  Google Scholar 

  14. Connes A. Cohomologie cyclique et foncteur Extn, C.R.Acad. Sci. Paris, serie I, 296 (1983), 953–958.

    MathSciNet  MATH  Google Scholar 

  15. 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).

    MathSciNet  MATH  Google Scholar 

  16. 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).

    MathSciNet  MATH  Google Scholar 

  17. Golovin Yu.O. Homological properties of Hilbert modules over nest operator algebras, Mat. Zametki 41 (1987), 769–775 (in Russian).

    MathSciNet  MATH  Google Scholar 

  18. Effros E.G. Amenability and virtual diagonals for von Neumann algebras, J. Funct. Anal. v.78 (1988), 137–153.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Lazar A.J., Tsui S.-K., Wright S. A cohomological characterization of finite-dimensional C*-algebras, J. Operator Theory 14 (1985)

    Google Scholar 

  20. Choi M.-D., Effros E.G. Nuclear C*-algebras and injectivity: the general case, Indiana Univ. Math. J. 26(1977), 443–446.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1992 Springer-Verlag

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Helemskii, A.Y. (1992). From topological homology: algebras with different properties of homological triviality. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis - Studies and Applications V. Lecture Notes in Mathematics, vol 1520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084713

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  • DOI: https://doi.org/10.1007/BFb0084713

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55583-4

  • Online ISBN: 978-3-540-47223-0

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