Skip to main content
Log in

Cohomology of infinitesimal and discrete groups

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Andersen, H.H., Jantzen, J.C.: Cohomology of induced representations for algebraic groups Math. Ann.269, 487–525 (1984)

    Google Scholar 

  2. Borel, A.: Chevalley groups. In: Seminar on algebraic groups and related finite groups. Lect. Notes Math. 131. Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  3. Bourbaki, N.: Groupes et algèbres de Lie. I. Paris: Hermann 1971

    Google Scholar 

  4. Bourbaki, N.: Groupes et algèbres de Lie. IV–VI. Paris: Hermann 1968

    Google Scholar 

  5. Carter, R.: Simple groups of Lie type. New York: Wiley 1972

    Google Scholar 

  6. Cline, E., Parshall, B., Scott, L.: Cohomology, hyperalgebras, and representations. J. Algebra63, 98–123 (1980)

    Google Scholar 

  7. Cline, E., Patshall, B., Scott, L.: A Mackey imprimitivity theory for algebraic groups Math. Z.182, 447–471 (1983)

    Google Scholar 

  8. Cline, E., Parshall, B., Scott, L.: On injective modules for infinitesimal algebraic groups. I. J. London Math. Soc. (2)31, 211–291 (1985)

    Google Scholar 

  9. Cline, E., Parshall, B., Scott, L., Kallen, W. van der: Rational and generic cohomology. Invent. Math.39, 143–163 (1977)

    Google Scholar 

  10. Donkin, S.: Rational representations of algebraic groups: Tensor products and filtrations. Lec. Notes Math. 1140. Berlin, Heidelberg, New York: Springer 1985

    Google Scholar 

  11. Evens, L.: The cohomology ring of a finite group. Trans. Am. Math. Soc.101, 224–239 (1961)

    Google Scholar 

  12. Dwyer, W.: Homology of integral upper-triangular matrices. Proc. A.M.S.84, 523–528 (1985)

    Google Scholar 

  13. Friedlander, E., Parshall, B.: Etale cohomology of reductive groups. AlgebraicK-theory, Evanston 1980. Lect. Notes Math. 854. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

  14. Friedlander, E., Parshall, B.: Cohomology of algebraic and related finite groups. Invent. Math.74, 85–117 (1983)

    Google Scholar 

  15. Friedlander, E., Parshall, B.: Cohomology of Lie algebras and algebraic groups. Am. J. Math. (to appear)

  16. Friedlander, E., Parshall, B.: Limits of infinitesimal group cohomology. To appear in Annals of Math. Studies

  17. Greub, W., Halperin, S., Vanstone, R.: Connections, curvature, and cohomology. III. London, New York: Academic Press 1976

    Google Scholar 

  18. Hilton, P., Stammbach, U.: A course in homological algebra. Berlin, Heidelberg, New York: Springer 1971

    Google Scholar 

  19. Hochschild, G.: Cohomology of restricted Lie algebras. Am. J. Math.76, 555–580 (1954)

    Google Scholar 

  20. Humphreys, J.: Modular representations of classical Lie algebras and semisimple groups. J. Algebra19, 51–79 (1971)

    Google Scholar 

  21. Jantzen, J.C.: Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne. J. Reine Angew. Math.317, 159–199 (1980)

    Google Scholar 

  22. Kostant, B.: Lie algebra cohomology and the generalized Borel-Weil theorem. Ann. Math.74, 329–387 (1961)

    Google Scholar 

  23. Lambe, L., Priddy, S.: Cohomology of nilmanifolds and torsion free, nilpotent groups. Trans. Am. Math. Soc.273, 39–55 (1982)

    Google Scholar 

  24. May, J.P.: The cohomology of restricted Lie algebras and of Hopf algebras. J. Algebra3, 123–146 (1966)

    Google Scholar 

  25. Nomizu, K.: On the cohomology of compact homogeneous spaces of nilpotent Lie groups. Ann. Math.59, 531–538 (1954)

    Google Scholar 

  26. Quillen, D.: On the associated graded ring of a group ring. J. Algebra10, 411–418 (1968)

    Google Scholar 

  27. Warner, G.: Harmonic analysis on semisimple Lie groups. I. Berlin, Heidelberg, New York: Springer 1972

    Google Scholar 

  28. Wilkerson, C.: The cohomology algebras of finite dimensional Hopf algebras. Trans. Am. Math. Soc.264, 137–150 (1981)

    Google Scholar 

  29. Zeeman, E.: A proof of the comparison theorem for spectral sequences. Proc. Camb. Phil. Soc.59, 57–62 (1957)

    Google Scholar 

  30. Koppinen, M.: Decomposing and lifting hyperalgebras. Turku thesis (1983)

  31. Brown, K., Dror, E.: The Artin-Rees property in homology. Isr. J. Math.22, 93–109 (1975)

    Google Scholar 

  32. Grünefelder, L.: On the homology of filtered and graded rings. J. Pure App. Algebra14, 21–37 (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported by the National Science Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

Friedlander, E.M., Parshall, B.J. Cohomology of infinitesimal and discrete groups. Math. Ann. 273, 353–374 (1986). https://doi.org/10.1007/BF01450727

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01450727

Keywords

Navigation