Comparison of Homologies and Automatic Extensions of Invariant Distributions

• Published in: Acta mathematica scientia Vol. 43; no. 4; pp. 1561 - 1570
• Main Author: Chen, Yangyang
• Format: Journal Article
• Language: English
• 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

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...