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

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• 作者：Masoud Sabzevari (1) (5)
  Amir Hashemi (2) (5)
  Benyamin M.-Alizadeh (3)
  Jo?l Merker (4)
  
• 关键词：differential algebra ; differential polynomial ring ; Ritt reduction algorithm ; Rosenfeld ; Gr?bner algorithm ; CR ; manifolds ; Lie algebras of infinitesimal CR ; automorphisms ; 68U05 ; 32M05 ; 32V40 ; 12H05
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：57
• 期：9
• 页码：1811-1834
• 全文大小：368 KB
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• 作者单位：Masoud Sabzevari (1) (5)
  Amir Hashemi (2) (5)
  Benyamin M.-Alizadeh (3)
  Jo?l Merker (4)
  
  1. Department of Pure Mathematics, University of Shahrekord, 88186-34141, Shahrekord, Iran
  5. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5746, Tehran, Iran
  2. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran
  3. School of Mathematics and Computer Sciences, Damghan University, P.O.Box 3671641167, Damghan, Iran
  4. Départment de Mathématiques d’Orsay, Batiment 425 Faculté des Sciences, Université Paris XI-Orsay, F-91405, Orsay Cedex, France
  
• ISSN：1869-1862

文摘

We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in ?sup class="a-plus-plus">9 by 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’s. Before 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 ?1. Also, 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.