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

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An Erratum to this article was published on 01 April 2005

Abstract

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.

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  1. Institute of Mathematics, Warsaw University, Warsaw, Poland

    P. Mormul

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  1. P. Mormul
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An erratum to this article can be found at http://dx.doi.org/10.1007/s10958-005-0347-0.

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Mormul, P. Kumpera-Ruiz algebras in Goursat flags are optimal in small lengths. J Math Sci 126, 1614–1629 (2005). https://doi.org/10.1007/s10958-005-0051-0

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