Hausdorffness of certain nilpotent cohomology spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909677983367168 |
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| author | Januszewski, Fabian Sun, Binyong Ying, Hao |
| author_facet | Januszewski, Fabian Sun, Binyong Ying, Hao |
| contents | Let $(π,V)$ be a smooth representation of a compact Lie group $G$ on a quasi-complete locally convex complex topological vector space. We show that the Lie algebra cohomology space $\mathrm{H} ^\bullet(\mathfrak{u}, V)$ and the Lie algebra homology space $\mathrm{H}_\bullet(\mathfrak{u}, V)$ are both Hausdorff, where $\mathfrak{u}$ is the nilpotent radical of a parabolic subalgebra of the complexified Lie algebra $\mathfrak{g}$ of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02799 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hausdorffness of certain nilpotent cohomology spaces Januszewski, Fabian Sun, Binyong Ying, Hao Representation Theory 22E46, 17B56 Let $(π,V)$ be a smooth representation of a compact Lie group $G$ on a quasi-complete locally convex complex topological vector space. We show that the Lie algebra cohomology space $\mathrm{H} ^\bullet(\mathfrak{u}, V)$ and the Lie algebra homology space $\mathrm{H}_\bullet(\mathfrak{u}, V)$ are both Hausdorff, where $\mathfrak{u}$ is the nilpotent radical of a parabolic subalgebra of the complexified Lie algebra $\mathfrak{g}$ of $G$. |
| title | Hausdorffness of certain nilpotent cohomology spaces |
| topic | Representation Theory 22E46, 17B56 |
| url | https://arxiv.org/abs/2501.02799 |