Pursell-Shanks type theorem for orbit spaces of G-manifolds

DOI10.2977/prims/1195183575zbMath0519.57033OpenAlexW2091454998MaRDI QIDQ1054329

Kōjun Abe

Publication date: 1982

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195183575

zbMATH Keywords

diffeomorphismLie algebra isomorphism between Lie algebras of all vector fields with compact support on paracompact connected manifoldsLie algebra of smooth vector fields on the orbit spacePursell-Shanks theorem for orbit spaces of G-manifoldssmooth structure of the orbit spacestrata preserving diffeomorphismstrata preserving vector fieldsstratification of orbit space

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Compact Lie groups of differentiable transformations (57S15) Infinite-dimensional Lie (super)algebras (17B65) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Differential topological aspects of diffeomorphisms (57R50)

Related Items

Lie algebraic characterization of manifolds, On Lie algebras of vector fields on smooth orbifolds, Derivations of the Lie algebras of differential operators

Cites Work

• Lifting smooth homotopies of orbit spaces
• Pursell-Shanks type theorem for free G-manifolds
• Smooth functions invariant under the action of a compact Lie group
• Lie algebra of vector fields and complex structure
• Lifting isotopies from orbit spaces
• Infinite dimensional Lie transformation groups
• Smooth G-manifolds as collections of fiber bundles
• Local Contractions and a Theorem of Poincare
• Covering smooth homotopies of orbit spaces
• On Lie algebras of vector fields with invariant submanifolds
• The Lie Algebra of a Smooth Manifold