Applications of differential algebra for computing Lie algebras of infinitesimal CR-automorphisms

作     者：SABZEVARI Masoud HASHEMI Amir M.-ALIZADEH Benyamin MERKER Jel 

作者机构：Department of Pure MathematicsUniversity of Shahrekord School of MathematicsInstitute for Research in Fundamental Sciences (IPM) Department of Mathematical SciencesIsfahan University of Technology School of Mathematics and Computer SciencesDamghan University Dpartment de Mathmatiques d'OrsayBatiment 425Facult des SciencesUniversit Paris XI-Orsay 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2014年第57卷第9期

页      面：1811-1834页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the Center for International Scientific Studies and Collaboration(CISSC)and French Embassy in Tehran The resend of the first and second authors was in part supported by grants from IPM(Grant Nos.91530040 and 92550420) 

主　　题：differential algebra differential polynomial ring Ritt reduction algorithm Rosenfeld-Grbner algorithm CR-manifolds Lie algebras of infinitesimal CR-automorphisms 

摘      要：We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C9by employing differential algebra computer tools—mostly within the Maple package DifferentialAlgebra—in order to automate the handling of the arising highly complex linear systems of PDE’*** treating these new examples which prolong previous works of Beloshapka,of Shananina and of Mamai,we provide general formulas for the explicitation of the concerned PDE systems that are valid in arbitrary codimension k 1 and in any CR dimension n ***,we show how Ritt’s reduction algorithm can be adapted to the case under interest,where the concerned PDE systems admit so-called complex conjugations.