Lie algebras of smooth sections

2008/03/19 by Hasan Gündoğan, Gündoğan, Hasan
Mathematics · #17B65 #17B66 #22E67 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.DG #math.RA #msc:17B65 #msc:17B66 #msc:22E67

paper · pdf · doi:10.48550/arxiv.0803.2800

openalex publication_date 2008/03/19 · arxiv created 2010/02/11 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Lie algebras of smooth sections are Lie algebras obtained from bundles of Lie algebras, where the latter are vector bundles of which the fibers are Lie algebras. We also consider the C^k-sections for k ∈ ℕ. This paper studies the derivations, the centroid and the isomorphisms of such Lie algebras and generalizes some facts from Pierre Lecomte's publications in 1979 and 1980 to the case where the fiber is perfect or centerfree and it gives some more explicit proofs.

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