Finite-dimensional $\mathbb{Z}$-graded Lie algebras
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908428846235648 |
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| author | Gould, Mark D. Isaac, Phillip S. Marquette, Ian Rasmussen, Jorgen |
| author_facet | Gould, Mark D. Isaac, Phillip S. Marquette, Ian Rasmussen, Jorgen |
| contents | We investigate the structure and representation theory of finite-dimensional $\mathbb{Z}$-graded Lie algebras, including the corresponding root systems and Verma, irreducible, and Harish-Chandra modules. This extends the familiar theory for finite-dimensional semisimple Lie algebras to a much wider class of Lie algebras, and opens up for advances and applications in areas relying on ad-hoc approaches. Physically relevant examples are afforded by the Heisenberg and conformal Galilei algebras, including the Schrödinger algebras, whose $\mathbb{Z}$-graded structures are yet to be fully exploited. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-dimensional $\mathbb{Z}$-graded Lie algebras Gould, Mark D. Isaac, Phillip S. Marquette, Ian Rasmussen, Jorgen Representation Theory High Energy Physics - Theory Mathematical Physics We investigate the structure and representation theory of finite-dimensional $\mathbb{Z}$-graded Lie algebras, including the corresponding root systems and Verma, irreducible, and Harish-Chandra modules. This extends the familiar theory for finite-dimensional semisimple Lie algebras to a much wider class of Lie algebras, and opens up for advances and applications in areas relying on ad-hoc approaches. Physically relevant examples are afforded by the Heisenberg and conformal Galilei algebras, including the Schrödinger algebras, whose $\mathbb{Z}$-graded structures are yet to be fully exploited. |
| title | Finite-dimensional $\mathbb{Z}$-graded Lie algebras |
| topic | Representation Theory High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2507.00384 |