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.
作者
陈阳洋
Yangyang CHEN(School of Sciences,Jiangnan University,Wuxi 214122,China)
基金
the Fundamental Research Funds for the Central Universities(JUSRP121045)
the NSF of Jiangsu Province(BK20221057)。
