{"abstract":[{"text":"Let $(\\pi,V)$ be a smooth representation of a compact Lie group $G$ on a\r\nquasi-complete locally convex complex topological vector space. We show that\r\nthe Lie algebra cohomology space $\\mathrm{H} ^\\bullet(\\mathfrak{u}, V)$ and the\r\nLie algebra homology space $\\mathrm{H}_\\bullet(\\mathfrak{u}, V)$ are both\r\nHausdorff, where $\\mathfrak{u}$ is the nilpotent radical of a parabolic\r\nsubalgebra of the complexified Lie algebra $\\mathfrak{g}$ of $G$.","lang":"eng"}],"language":[{"iso":"eng"}],"user_id":"81636","author":[{"first_name":"Fabian","last_name":"Januszewski","full_name":"Januszewski, Fabian"},{"last_name":"Sun","first_name":"Binyong","full_name":"Sun, Binyong"},{"full_name":"Ying, Hao","first_name":"Hao","last_name":"Ying"}],"status":"public","citation":{"apa":"Januszewski, F., Sun, B., &#38; Ying, H. (2025). Hausdorffness of certain nilpotent cohomology spaces. In <i>arXiv:2501.02799</i>.","chicago":"Januszewski, Fabian, Binyong Sun, and Hao Ying. “Hausdorffness of Certain Nilpotent Cohomology Spaces.” <i>ArXiv:2501.02799</i>, 2025.","short":"F. Januszewski, B. Sun, H. Ying, ArXiv:2501.02799 (2025).","bibtex":"@article{Januszewski_Sun_Ying_2025, title={Hausdorffness of certain nilpotent cohomology spaces}, journal={arXiv:2501.02799}, author={Januszewski, Fabian and Sun, Binyong and Ying, Hao}, year={2025} }","mla":"Januszewski, Fabian, et al. “Hausdorffness of Certain Nilpotent Cohomology Spaces.” <i>ArXiv:2501.02799</i>, 2025.","ama":"Januszewski F, Sun B, Ying H. Hausdorffness of certain nilpotent cohomology spaces. <i>arXiv:250102799</i>. Published online 2025.","ieee":"F. Januszewski, B. Sun, and H. Ying, “Hausdorffness of certain nilpotent cohomology spaces,” <i>arXiv:2501.02799</i>. 2025."},"date_created":"2025-01-07T19:31:01Z","type":"preprint","title":"Hausdorffness of certain nilpotent cohomology spaces","year":"2025","date_updated":"2025-01-07T19:32:33Z","external_id":{"arxiv":["2501.02799"]},"publication":"arXiv:2501.02799","_id":"58096"}