Canonical forms for matrices of Saletan contractions

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Popovych, Dmytro R.^1

Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, Building 7, Academician Glushkov Av., Kyiv

03127, Ukraine^1

关键词: Canonical form;    Change of basis;    Codimension;    Lie Algebra;    Limit values;    Matrix functions;    One parts;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012012/pdf
DOI  :  10.1088/1742-6596/621/1/012012

来源: IOP

【 摘 要 】

We show that each Saletan (linear) contraction can be realized, up to change of bases of the initial and the target Lie algebras, by a matrix-function that is completely defined by a partition of the dimension of Fitting component of its value at the limit value of the contraction parameter. The codimension of the Fitting component and this partition constitute the signature of the Saletan contraction. We study Saletan contractions with Fitting component of maximal dimension and trivial one-part partition. All contractions of such kind in dimension three are completely classified.