Mathematische Zeitschrift

, Volume 221, Issue 1, pp 113–137 | Cite as

Grothendieck groups of invariant rings: linear actions of finite groups

  • Kenneth A. Brown
  • Martin Lorenz
Article

Keywords

Exact Sequence Finite Group Noetherian Ring Grothendieck Group Power Series Ring 
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.

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References

  1. [A-R1]
    M. Auslander and I. Reiten, Grothendieck groups of algebras with nilpotent annihilators,Proc. Amer. Math. Soc. 103 (1988), 1022–1024MATHCrossRefMathSciNetGoogle Scholar
  2. [A-R2]
    M. Auslander and I. Reiten, Grothendieck groups of algebras and orders,J. Pure and Appl. Algebra 39 (1986), 1–51MATHCrossRefMathSciNetGoogle Scholar
  3. [B]
    H. Bass,Algebraic K-theory, Benjamin, New York, 1968MATHGoogle Scholar
  4. [Br-L]
    K.A. Brown and M. Lorenz, Grothendieck groups of invariant rings and of group rings,J. Algebra 166 (1994), 423–454MATHCrossRefMathSciNetGoogle Scholar
  5. [Br-L1]
    K.A. Brown and M. Lorenz, Grothendieck groups of invariant rings: filtrations,Proc. London Math. Soc. 67 (1993), 516–546MATHCrossRefMathSciNetGoogle Scholar
  6. [Br-L2]
    K.A. Brown and M. Lorenz, Grothendieck groups of invariant rings: examples, University of Glasgow preprint, 1992, to appearComm. in Algebra Google Scholar
  7. [C-R]
    C.W. Curtis and I. Reiner,Methods of Representation Theory, Wiley-Interscience, New York, 1981MATHGoogle Scholar
  8. [H-S]
    J. Herzog and H. Sanders, The Grothendieck group of invariant rings and of simple hypersurface singularities, In: Lecture Notes in Math. No. 1273,Singularities, Representation of Algebras, and Vector Bundles, ed. G.-M. Greuel and G. Trautmann, Springer-Verlag, Berlin, 1987, pp. 131–149CrossRefGoogle Scholar
  9. [H-M-W]
    J. Herzog, E. Marcos and R. Waldi, On the Grothendieck group of a quotient singularity defined by a finite abelian group,J. Algebra 149 (1992), 122–138MATHCrossRefMathSciNetGoogle Scholar
  10. [H]
    T. Hodges, EquivariantK-theory for Noetherian rings,J. London Math. Soc. 39 (1989), 414–426MATHCrossRefMathSciNetGoogle Scholar
  11. [M]
    E.D.N. Marcos, Grothendieck groups of quotient singularities,Trans. Amer. Math. Soc 332 (1992) 93–119MATHCrossRefMathSciNetGoogle Scholar
  12. [McC-R]
    J.C. McConnell and J.C. Robson,Noncommutative Noetherian Rings Wiley-Interscience, New York, 1987MATHGoogle Scholar
  13. [P]
    I.B.S. Passi, Polynomial maps of groups,J. Algebra 9 (1968), 121–151MATHCrossRefMathSciNetGoogle Scholar
  14. [Q]
    D. Quillen, Higher algebraicK-theory I, In: Lecture Notes in Math. No. 341,Algebraic K-Theory I, ed. H. Bass, Springer-Verlag, Berlin-Heidelberg, 1973, pp. 85–147Google Scholar
  15. [S]
    B. Singh, Invariants of finite groups acting on local unique factorization domains,J. Indian Math. Soc. 34 (1970), 31–38MathSciNetGoogle Scholar
  16. [Sp]
    T.A. Springer,Invariant Theory, Lecture Notes in Math. No. 585, Springer-Verlag, Berlin, 1977MATHGoogle Scholar
  17. [W]
    J.A. Wolf,Spaces of Constant Curvature, 5th Ed., Publish or Perish, Wilmington, 1984Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Kenneth A. Brown
    • 1
  • Martin Lorenz
    • 2
  1. 1.Department of MathematicsUniversity of Glasgow, University GardensGlasgowUnited Kingdom
  2. 2.Department of MathematicsTemple UniversityPhiladelphiaUSA

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