HAL CCSD
Lie algebras of infinitesimal CR automorphisms of weighted homogeneous and homogeneous CR-generic submanifolds of C^N
Sabzevari, Masoud
Hashemi, Amir
Alizadeh, Benyamin
Merker, Joël
Department of Pure Mathematics [Shahrekord] ; Shahrekord University
Isfahan University of Technology
Damghan University
Laboratoire de Mathématiques d'Orsay (LMO) ; Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
International audience
ISSN: 0354-5180
Filomat
University of Nis
hal-03286255
https://universite-paris-saclay.hal.science/hal-03286255
https://universite-paris-saclay.hal.science/hal-03286255/document
https://universite-paris-saclay.hal.science/hal-03286255/file/46.pdf
https://universite-paris-saclay.hal.science/hal-03286255
Filomat, 2016, 30 (6), pp.1387-1411. ⟨10.2298/fil1606387s⟩
DOI: 10.2298/fil1606387s
info:eu-repo/semantics/altIdentifier/doi/10.2298/fil1606387s
http://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/1189
en
CR manifolds
CR automorphism algebra
Comprehensive Gröbner system
2010 MSC: Primary 32V40; Secondary 68W30
[MATH]Mathematics [math]
info:eu-repo/semantics/article
Journal articles
We consider the significant class of homogeneous CR manifolds represented by some weighted homogeneous polynomials and we derive some plain and useful features which enable us to set up a fast effective algorithm to compute homogeneous components of their Lie algebras of infinitesimal CR automorphisms. This algorithm mainly relies upon a natural gradation of the sought Lie algebras, and it also consists in treating separately the related graded components. While classical methods are based on constructing and solving some associated pde systems which become time consuming as soon as the number of variables increases, the new method presented here is based on plain techniques of linear algebra. Furthermore, it benefits from a divide-and-conquer strategy to break down the computations into some simpler subcomputations. Also, we consider the new and effective concept of comprehensive Gröbner systems which provides us some powerful tools to treat the computations in the much complicated parametric case. The designed algorithm is also implemented in the Maple software, what required also implementing a recently designed algorithm of Kapur et al.
2016
info:eu-repo/semantics/OpenAccess