Lie algebras of infinitesimal CR automorphisms of weighted homogeneous and homogeneous CR-generic submanifolds of C^N
Autor: | Amir Hashemi, Joel Merker, Masoud Sabzevari, Benyamin M.-Alizadeh |
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Přispěvatelé: | 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) |
Jazyk: | angličtina |
Rok vydání: | 2016 |
Předmět: |
Class (set theory)
CR automorphism algebra General Mathematics Computation Infinitesimal 010102 general mathematics Comprehensive Gröbner system 010103 numerical & computational mathematics Automorphism 01 natural sciences 2010 MSC: Primary 32V40 Secondary 68W30 Set (abstract data type) Algebra Lie algebra Linear algebra ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION CR manifolds 0101 mathematics [MATH]Mathematics [math] Mathematics Parametric statistics |
Zdroj: | Filomat Filomat, University of Nis, 2016, 30 (6), pp.1387-1411. ⟨10.2298/fil1606387s⟩ |
ISSN: | 0354-5180 |
DOI: | 10.2298/fil1606387s⟩ |
Popis: | 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 Gr?bner 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. |
Databáze: | OpenAIRE |
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