COMPARISON OF HOMOLOGIES AND AUTOMATIC EXTENSIONS OF INVARIANT DISTRIBUTIONS  

作　　者：陈阳洋 Yangyang CHEN(School of Sciences,Jiangnan University,Wuxi 214122,China)

机构地区：[1]School of Sciences,Jiangnan University,Wuxi 214122,China

出　　处：《Acta Mathematica Scientia》2023年第4期1561-1570,共10页数学物理学报（B辑英文版）

基　　金：the Fundamental Research Funds for the Central Universities(JUSRP121045);the NSF of Jiangsu Province(BK20221057)。

摘　　要：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.Letχbe 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.

关 键 词：Schwartz functions Lie algebra homology Hausdorffness Schwartz distributions automatic extensions 

分 类 号：O152.5[理学—数学]