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Ukrainian Mathematical Journal

, Volume 64, Issue 7, pp 1019–1035 | Cite as

Local deformations of positive-definite quadratic forms

  • V. M. Bondarenko
  • V. V. Bondarenko
  • Yu. N. Pereguda
Article
  • 64 Downloads

We give a complete description of real numbers that are P-limit numbers for integer-valued positive-definite quadratic forms with unit coefficients of the squares. It is shown that each of these P-limit numbers is realized in the Tits quadratic form of a certain Dynkin diagram.

Keywords

Quadratic Form Linear Transformation Symmetric Matrix Local Deformation Dynkin Diagram 
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. 1.
    V. M. Bondarenko and Yu. M. Pereguda, “On P-numbers of quadratic forms,” in: Geometry, Topology, and Their Applications, Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences, 6, No. 2 (2009), pp. 474–477.Google Scholar
  2. 2.
    P. Gabriel, “Unzerlegbare Darstellungen,” Manuscr. Math., 6, 71–103, 309 (1972).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    S. Lang, Algebra, Addison, Reading (1965).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • V. M. Bondarenko
    • 1
  • V. V. Bondarenko
    • 1
  • Yu. N. Pereguda
    • 2
  1. 1.KievUkraine
  2. 2.KievUkraine

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