Deformations of semi-direct products
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913624606375936 |
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| author | Alvarez, Maria Alejandra Rivière, Salim Rojas, Nadina Vera, Sonia Wagemann, Friedrich |
| author_facet | Alvarez, Maria Alejandra Rivière, Salim Rojas, Nadina Vera, Sonia Wagemann, Friedrich |
| contents | We exhibit in this article a contraction of the direct product Lie algebra $g\oplus g$ of a finite-dimensional complex Lie algebra $g$ onto the semi-direct product Lie algebra $g\rtimes g$, where the first factor $g$ is viewed as a trivial Lie algebra and as the adjoint $g$-module. This contraction gives rise to a non-zero cohomology class in the second cohomology space. We generalize to the setting of $h\oplus g$ and $h\rtimes g$ with respect to a given crossed module of Lie algebras $h\to g$. We give many examples to illustrate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17914 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformations of semi-direct products Alvarez, Maria Alejandra Rivière, Salim Rojas, Nadina Vera, Sonia Wagemann, Friedrich Quantum Algebra K-Theory and Homology 17B56 We exhibit in this article a contraction of the direct product Lie algebra $g\oplus g$ of a finite-dimensional complex Lie algebra $g$ onto the semi-direct product Lie algebra $g\rtimes g$, where the first factor $g$ is viewed as a trivial Lie algebra and as the adjoint $g$-module. This contraction gives rise to a non-zero cohomology class in the second cohomology space. We generalize to the setting of $h\oplus g$ and $h\rtimes g$ with respect to a given crossed module of Lie algebras $h\to g$. We give many examples to illustrate our results. |
| title | Deformations of semi-direct products |
| topic | Quantum Algebra K-Theory and Homology 17B56 |
| url | https://arxiv.org/abs/2412.17914 |