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...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’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.展开更多
基金supported by the Center for International Scientific Studies and Collaboration(CISSC)and French Embassy in TehranThe resend of the first and second authors was in part supported by grants from IPM(Grant Nos.91530040 and 92550420)
文摘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’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.
