Comparison of Homologies and Automatic Extensions of Invariant Distributions

Let G be a reductive Nash group, acting on a Nash manifold X . Let Z be a G -stable closed Nash submanifold of X and denote by U the complement of Z in X . Let χ be a character of G and denote by g the complexified Lie algebra of G . We give a sufficient condition for the natural linear map H k ( g...

Full description

Saved in:
Bibliographic Details
Published inActa mathematica scientia Vol. 43; no. 4; pp. 1561 - 1570
Main Author Chen, Yangyang
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.07.2023
School of Sciences,Jiangnan University,Wuxi 214122,China
Subjects
Analysis
Mathematics
Mathematics and Statistics
Schwartz distributions
Hausdorffness
automatic extensions
Schwartz functions
46T30
22E20
Lie algebra homology
Schwartz distribu-tions
Online AccessGet full text

Cover

More Information
Summary:Let G be a reductive Nash group, acting on a Nash manifold X . Let Z be a G -stable closed Nash submanifold of X and denote by U the complement of Z in X . Let χ be a character of G and denote by g the complexified Lie algebra of G . We give a sufficient condition for the natural linear map H k ( g , S ( U ) ⊗ χ ) → H k ( g , S ( X ) ⊗ χ ) between the Lie algebra homologies of Schwartz functions to be an isomorphism. For k = 0, by considering the dual, we obtain the automatic extensions of g -invariant (twisted by - χ ) Schwartz distributions.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-023-0407-x