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- Title
Algebraic Structures on Smooth Vector Fields.
- Authors
Alkinani, Amnah A.; Alghamdi, Ahmad M.
- Abstract
The aim of this work is to investigate some algebraic structures of objects which are defined and related to a manifold. Consider L to be a smooth manifold and Γ ∞ (T L) to be the module of smooth vector fields over the ring of smooth functions C ∞ (L) . We prove that the module Γ ∞ (T L) is projective and finitely generated, but it is not semisimple. Therefore, it has a proper socle and nonzero Jacobson radical. Furthermore, we prove that this module is reflexive by showing that it is isomorphic to its bidual. Additionally, we investigate the structure of the Lie algebra of smooth vector fields. We give some questions and open problems at the end of the paper. We believe that our results are important because they link two different disciplines in modern pure mathematics.
- Subjects
VECTOR fields; JACOBSON radical; LIE algebras; VECTOR algebra; SMOOTHNESS of functions; OPEN-ended questions
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 12, p2150
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15122150