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arXiv · 2502.12475

On the variety of Lie algebras endowed with complex structures: degenerations and deformations

Edison Alberto Fernández-Culma·Nadina Rojas
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Abstract

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}) $.

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Edison Alberto Fernández-Culma, Nadina Rojas. 2025-02-18. On the variety of Lie algebras endowed with complex structures: degenerations and deformations. https://arxiv.org/abs/2502.12475

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