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

Benyamin M.-Alizadeh (1) , Masoud Sabzevari (2, 3) , Amir Hashemi (4, 3) , Joël Merker (5)

1 Damghan University
2 Department of Pure Mathematics [Shahrekord]
3 IPM - Institute for Research in Fundamental Sciences [Tehran]
4 Isfahan University of Technology
5 LMO - Laboratoire de Mathématiques d'Orsay

We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C^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.

Mots clés: differential algebra; differential polynomial ring; Ritt reduction algorithm; Rosenfeld-Gröbner algorithm; CR-manifolds; Lie algebras of infinitesimal CR-automorphisms; differential algebra

Domaines: Mathématiques [math]

Benyamin M.-Alizadeh, Masoud Sabzevari, Amir Hashemi, Joël Merker. Applications of differential algebra for computing Lie algebras of infinitesimal CR-automorphisms. Science China Mathematics, 2014, 57 (9), pp.1811-1834. ⟨10.1007/s11425-013-4751-5⟩. ⟨hal-03286239⟩