{"language":[{"iso":"eng"}],"type":"journal_article","date_updated":"2025-11-17T13:52:50Z","title":"Hausdorffness of certain nilpotent cohomology spaces","author":[{"last_name":"Januszewski","first_name":"Fabian","full_name":"Januszewski, Fabian"},{"full_name":"Sun, Binyong","first_name":"Binyong","last_name":"Sun"},{"full_name":"Ying, Hao","first_name":"Hao","last_name":"Ying"}],"citation":{"mla":"Januszewski, Fabian, et al. “Hausdorffness of Certain Nilpotent Cohomology Spaces.” <i>Journal of Functional Analysis</i>, vol. 289, no. 10, 2025.","ieee":"F. Januszewski, B. Sun, and H. Ying, “Hausdorffness of certain nilpotent cohomology spaces,” <i>Journal of Functional Analysis</i>, vol. 289, no. 10, 2025.","ama":"Januszewski F, Sun B, Ying H. Hausdorffness of certain nilpotent cohomology spaces. <i>Journal of Functional Analysis</i>. 2025;289(10).","apa":"Januszewski, F., Sun, B., &#38; Ying, H. (2025). Hausdorffness of certain nilpotent cohomology spaces. <i>Journal of Functional Analysis</i>, <i>289</i>(10).","short":"F. Januszewski, B. Sun, H. Ying, Journal of Functional Analysis 289 (2025).","chicago":"Januszewski, Fabian, Binyong Sun, and Hao Ying. “Hausdorffness of Certain Nilpotent Cohomology Spaces.” <i>Journal of Functional Analysis</i> 289, no. 10 (2025).","bibtex":"@article{Januszewski_Sun_Ying_2025, title={Hausdorffness of certain nilpotent cohomology spaces}, volume={289}, number={10}, journal={Journal of Functional Analysis}, author={Januszewski, Fabian and Sun, Binyong and Ying, Hao}, year={2025} }"},"volume":289,"issue":"10","abstract":[{"lang":"eng","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 $G$."}],"date_created":"2025-01-07T19:31:01Z","status":"public","_id":"58096","external_id":{"arxiv":["2501.02799"]},"intvolume":"       289","year":"2025","publication":"Journal of Functional Analysis","user_id":"81636","publication_identifier":{"issn":["0022-1236"]}}