Tanaka rigidity of graph Lie algebras
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914675491340288 |
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| author | Molina, Mauricio Godoy |
| author_facet | Molina, Mauricio Godoy |
| contents | We give sufficient conditions on a labeled direct graph to determine whether the Tanaka prolongation of its associated Lie algebra is infinite-dimensional. In the case that all directed edges are labeled differently, the corresponding graph Lie algebra is of infinite type if and only if the graph has a vertex of degree one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tanaka rigidity of graph Lie algebras Molina, Mauricio Godoy Differential Geometry Combinatorics Rings and Algebras 53C24, 17B30, 17B66, 05C20, 05C25 We give sufficient conditions on a labeled direct graph to determine whether the Tanaka prolongation of its associated Lie algebra is infinite-dimensional. In the case that all directed edges are labeled differently, the corresponding graph Lie algebra is of infinite type if and only if the graph has a vertex of degree one. |
| title | Tanaka rigidity of graph Lie algebras |
| topic | Differential Geometry Combinatorics Rings and Algebras 53C24, 17B30, 17B66, 05C20, 05C25 |
| url | https://arxiv.org/abs/2402.07873 |