Homology of Lie Algebras of Matrices

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 301)


One of the main properties of cyclic homology is its relationship with the homology of the Lie algebra of matrices. Explicitly it takes the following form.


Hopf Algebra Invariant Theory Leibniz Algebra Cyclic Homology Tensor Module 
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Bibliographical Comments on Chapter 10

  1. Koszul, J.L., Homologie et cohomologie des algèbres de Lie, Bull. Soc. Math. France 78 (1950), 65–127MathSciNetzbMATHGoogle Scholar
  2. Loday, J.-L., Quillen, D., Homologie cyclique et homologie de l’algèbre de Lie des matrices, C. R. Acad. Sci. Paris Sér. A-B 296 (1983), 295–297MathSciNetzbMATHGoogle Scholar
  3. Tsygan, B.L., The homology of matrix Lie algebras over rings and the Hochschild homology (en russe), Uspekhi Mat. Nauk 38 (1983), 217–218–Russ. Math. Survey 38 No. 2 (1983), 198–199Google Scholar
  4. Dwyer, W.G., Hsiang, W.C., Staffeldt, R.E., Pseudo-isotopy and invariant theory-I, Topology 19 (1980), 367–385.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Hsiang, W.-C., Staffeldt, R.E., A model for computing rational algebraic Ktheory of simply connected spaces, Invent. Math. 68 (1982), 227–239MathSciNetzbMATHCrossRefGoogle Scholar
  6. Carlsson, G.E., Cohen, R.L., Goodwillie, T., Hsiang, W.-C., The free loop space and the algebraic K-theory of spaces, K-theory 1 (1985), 53–82MathSciNetCrossRefGoogle Scholar
  7. Loday, J.-L., Procesi, C., Homology of symplectic and orthogonal algebras, Advances in Math. 69 (1988), 93–108MathSciNetzbMATHCrossRefGoogle Scholar
  8. Hanlon, P., On the complete GL(n,C)-decomposition of the stable cohomology of gln(A), Trans. Ams 308 (1988), 209–225. 90k: 17040MathSciNetGoogle Scholar
  9. Cuntz, J., Quillen, D., Algebra extensions and nonsingularity, preprint (1991). Cuvier, C., Homologie de Leibniz et homologie de Hochschild, C. R. Acad. Sci. Paris Sér. A-B 313 (1991), 569–572.Google Scholar
  10. Loday, J.-L., Pirashvili, T., Universal enveloping algebras of Leibniz algebras and (co)homology, preprint Strasbourg (1992).Google Scholar
  11. Aboughazi, R., Homologie restreinte des p-algèbres de Lie en degré deux, Ann. Inst. Fourier 39 (1989), 641–649.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeCentre National de la Recherche ScientifiqueStrasbourgFrance

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