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تسجيل مستخدم جديدSchwartz homologies of representations of almost linear Nash groups
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Let $G$ be an almost linear Nash group, namely, a Nash group which admits a Nash homomorphism with finite kernel to some $GL_k(mathbb R)$. A homology theory (the Schwartz homology) is established for the category of smooth Fre representations of $G$ of moderate growth. Frobenius reciprocity and Shapiros lemma are proved in this category. As an application, we give a criterion for automatic extensions of Schwartz homologies of Schwartz sections of a tempered $G$-vector bundle.
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