2002/03/05 by Askar Dzhumadil’daev, A. S. Dzhumadil'daev, Dzhumadil'daev, A. S.
Mathematics · Physics and Astronomy · #17B66 #17C50 #22E65 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Finite Group Theory Research #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math-ph #math.MP #math.QA #math.RA #msc:17B66 #msc:17C50 #msc:22E65
paper · pdf · doi:10.48550/arxiv.math/0203036
44 pages
openalex publication_date 2002/03/05 · arxiv created 2002/03/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An alternating sum of compositions of N vector fields is called N-commutator. In general N-commutator of N vector fields is no longer a vector field. Question: is it possible to find N=N(n), such that N-commutator of any vector fields in Vect(n) is once again a vector field. Theorem: n2+2n-2-commutator is a such one. A theory of N-commutators with emphasis on 5-and 6-commutators on two dimensional manifold is developed.