Skip to main content

From topological homology: algebras with different properties of homological triviality

  • Conference paper
  • First Online:
Global Analysis - Studies and Applications V

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

  • 338 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  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.

    Article  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.

    Article  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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Yuri G. Borisovich Yuri E. Gliklikh A. M. Vershik

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55583-4

  • Online ISBN: 978-3-540-47223-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics