Journal of Mathematical Sciences

, Volume 126, Issue 6, pp 1614–1629 | Cite as

Kumpera-Ruiz algebras in Goursat flags are optimal in small lengths

  • P. Mormul


Kumpera-Ruiz algebras of germs of Goursat distributions are nilpotent algebras with explicitly computable orders of nilpotence. At some points, called tangential, these orders coincide with the nonholonomy degrees (calculated earlier by Jean) of the ambient G. germs. At nontangential points (that mostly occur and are stratified into geometric classes of Jean, Montgomery, and Zhitomirskii), nonholonomy degrees are lesser, sometimes even much lesser. It is a well-known open question in the theory of G. distributions: whether Kumpera-Ruiz algebras realize the minimal possible nilpotence orders or not. In the present paper, in small lengths of the induced G. flags (up to 5 inclusively) and also for 8 nontangential classes in length 6 (among 18 nontangential existing in this length 6), we show that the answer to this question is affirmative: the nilpotence orders of Kumpera-Ruiz algebras cannot be lowered. This makes more probable that a general answer to the question is affirmative in the general case.


Small Length General Answer Computable Order Nilpotent Algebra Geometric Classis 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • P. Mormul
    • 1
  1. 1.Institute of MathematicsWarsaw UniversityWarsawPoland

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