On the variety of Lie algebras endowed with complex structures: degenerations and deformations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929718892167168 |
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| author | Fernández-Culma, Edison Alberto Rojas, Nadina |
| author_facet | Fernández-Culma, Edison Alberto Rojas, Nadina |
| contents | We study the space of Lie algebras equipped with left-invariant complex structures, $\mathcal{L}_{ J_{\tiny{\mbox{cn}}} }(\mathbb{R}^{2n}) $, with particular attention to their degenerations and deformations. To this end, we identify certain invariants that remain well-behaved under degenerations while preserving the complex structure. These concepts are then applied to the four-dimensional case. Additionally, we explore applications to the study of left-invariant Hermitian structures on Lie groups, and we discuss some aspects of the deformation theory within $ \mathcal{L}_{ J_{\tiny{\mbox{cn}}} }(\mathbb{R}^{2n}) $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the variety of Lie algebras endowed with complex structures: degenerations and deformations Fernández-Culma, Edison Alberto Rojas, Nadina Representation Theory Differential Geometry 17B99 We study the space of Lie algebras equipped with left-invariant complex structures, $\mathcal{L}_{ J_{\tiny{\mbox{cn}}} }(\mathbb{R}^{2n}) $, with particular attention to their degenerations and deformations. To this end, we identify certain invariants that remain well-behaved under degenerations while preserving the complex structure. These concepts are then applied to the four-dimensional case. Additionally, we explore applications to the study of left-invariant Hermitian structures on Lie groups, and we discuss some aspects of the deformation theory within $ \mathcal{L}_{ J_{\tiny{\mbox{cn}}} }(\mathbb{R}^{2n}) $. |
| title | On the variety of Lie algebras endowed with complex structures: degenerations and deformations |
| topic | Representation Theory Differential Geometry 17B99 |
| url | https://arxiv.org/abs/2502.12475 |