Prolongation rigidity of sub-free Lie algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910090887430144 |
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| author | Kruglikov, Boris |
| author_facet | Kruglikov, Boris |
| contents | We prove that if the 0-th Tanaka prolongation $\mathfrak{g}_0=\mathfrak{der}_0(\mathfrak{m})$ of a fundamental graded nilpotent Lie algebra $\mathfrak{m}=\mathfrak{g}_{-s}\oplus\dots\oplus\mathfrak{g}_{-1}$ is irreducible on $\mathfrak{g}_{-1}$, then $\mathfrak{m}$ is prolongation rigid: $\text{pr}_+(\mathfrak{m})=0$. The only exceptions are given by negative gradations of maximal parabolic subalgebras of a simple Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01643 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prolongation rigidity of sub-free Lie algebras Kruglikov, Boris Differential Geometry Representation Theory We prove that if the 0-th Tanaka prolongation $\mathfrak{g}_0=\mathfrak{der}_0(\mathfrak{m})$ of a fundamental graded nilpotent Lie algebra $\mathfrak{m}=\mathfrak{g}_{-s}\oplus\dots\oplus\mathfrak{g}_{-1}$ is irreducible on $\mathfrak{g}_{-1}$, then $\mathfrak{m}$ is prolongation rigid: $\text{pr}_+(\mathfrak{m})=0$. The only exceptions are given by negative gradations of maximal parabolic subalgebras of a simple Lie algebra. |
| title | Prolongation rigidity of sub-free Lie algebras |
| topic | Differential Geometry Representation Theory |
| url | https://arxiv.org/abs/2603.01643 |