Commentarii Mathematici Helvetici

, Volume 59, Issue 1, pp 565–591 | Cite as

Cyclic homology and the Lie algebra homology of matrices

  • Jean-Louis Loday
  • Daniel Quillen
Article

Keywords

Exact Sequence Hopf Algebra Spectral Sequence Characteristic Zero Cyclic Homology 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    S. Bloch,The dilogarithm and extensions of Lie algebras, in AlgebraicK-theory, Evanston 1980, Springer Lecture Note,854 (1981), 1–23.Google Scholar
  2. [2]
    H. Cartan andS. Eilenberg,Homological Algebra, Princeton University Press, 1956.Google Scholar
  3. [3]
    A. Connes,Non commutative differential geometry, Ch. II De Rham homology and non commutative algebra, preprint I.H.E.S. (1983).Google Scholar
  4. [4]
    —,Cohomologie cyclique et foncteurs Extn, Comptes Rendus Acad. Sc. Paris296 (1983), 953–958.MathSciNetMATHGoogle Scholar
  5. [5]
    G. Hochschild, B. Kostant andA. Rosenberg,Differential forms on regular affine algebras, Trans. A.M.S.102 (1962), 383–408.CrossRefMathSciNetMATHGoogle Scholar
  6. [6]
    W.-c. Hsiang andR. E. Staffeldt,A model for computing rational algebraic K-theory of simply connected spaces, Invent. Math.68 (1982), 227–239.CrossRefMathSciNetMATHGoogle Scholar
  7. [7]
    C. Kassel etJ.-L. Loday,Extensions centrales d'algèbres de Lie, Ann. Inst. Fourier32 (1982), 119–142.MathSciNetMATHGoogle Scholar
  8. [8]
    J.-L. Koszul,Homologie et cohomologie des algèbres de Lie, Bull. Soc. Math. France78 (1950), 65–127.MathSciNetMATHGoogle Scholar
  9. [9]
    J.-L. Loday etD. Quillen,Homologie cyclique et homologie de l'algèbre de Lie des matrices, Comptes Rendus Acad. Sc. Paris,296 (1983), 295–297.MathSciNetMATHGoogle Scholar
  10. [10]
    D. Quillen,Cohomology of groups, Actes Congrès International Math. 1970, t. 2, 47–51.Google Scholar
  11. [11]
    C. Soulé,Opérations en K-théorie algébrique, prépublication Paris VII, 1983.Google Scholar
  12. [12]
    B. L. Tsygan,Homology of matrix algebras over rings and the Hochschild homology (in Russian), Uspekhi Mat. Nauk, tom38 (1983), 217–218.MathSciNetMATHGoogle Scholar
  13. [13]
    H. Weyl,The classical groups, Princeton University Press, 1946.Google Scholar
  14. [14]
    R. K. Dennis andK. Igusa,Hochschild homology and the second obstruction for pseudo-isotopy, Springer Lecture Notes in Math.966 (1982), 7–58.MathSciNetCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag 1984

Authors and Affiliations

  • Jean-Louis Loday
    • 1
    • 2
  • Daniel Quillen
    • 1
    • 2
  1. 1.Institut de Recherche Mathématique AvancéeUniversité L. PasteurStrasbourgFrance
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations