Let $G$ be an almost linear Nash group, namely, a Nash group that admits a Nash homomorphism with finite kernel to some ${\mathrm GL}_k(\mathbb R)$. A smooth Fr\'{e}chet representation $V$ with moderate growth of $G$ is called homologically finite if the Schwartz homology ${\mathrm H}_{i}^{\mathcal{S}}(G;V)$ is finite dimensional for every $i\in{\mathbb Z}$. We show that the space of Schwartz sections $\Gamma^{\varsigma}(X,{\mathrm E})$ of a tempered $G$-vector bundle $(X,{\mathrm E})$ is homologically finite as a representation of $G$, under some mild assumptions.
1
School of Sciences, Harbin Institute of Technology, Shenzhen, P. R. China
2
School of Sciences, Jiangnan University, Wuxi, P. R. China
Yixin Bao; Yangyang Chen. Homological Finiteness of Representations of Almost Linear Nash Groups. Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 1045-1053. http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a10/
@article{JOLT_2021_31_4_a10,
author = {Yixin Bao and Yangyang Chen},
title = {Homological {Finiteness} of {Representations} of {Almost} {Linear} {Nash} {Groups}},
journal = {Journal of Lie Theory},
pages = {1045--1053},
year = {2021},
volume = {31},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a10/}
}
TY - JOUR
AU - Yixin Bao
AU - Yangyang Chen
TI - Homological Finiteness of Representations of Almost Linear Nash Groups
JO - Journal of Lie Theory
PY - 2021
SP - 1045
EP - 1053
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a10/
ID - JOLT_2021_31_4_a10
ER -
%0 Journal Article
%A Yixin Bao
%A Yangyang Chen
%T Homological Finiteness of Representations of Almost Linear Nash Groups
%J Journal of Lie Theory
%D 2021
%P 1045-1053
%V 31
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a10/
%F JOLT_2021_31_4_a10
