Locally conformal SKT almost abelian Lie algebras

2022/12/22 by Louis-Brahim Beaufort, Beaufort, Louis-Brahim, Anna Fino +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2212.11539

openalex publication_date 2022/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A locally conformal SKT (shortly LCSKT) structure is a Hermitian structure (J, g) whose Bismut torsion 3-form H satisfies the condition dH = α\wedge H, for some closed non-zero 1-form α. This condition was introduced in [6] as a generalization of the SKT (or pluriclosed) condition dH= 0. In this paper, we characterize the almost abelian Lie algebras admitting a Hermitian structure (J, g) such that dH = α\wedge H, for some closed 1-form α. As an application we classifiy LCSKT almost abelian Lie algebras in dimension 6. Finally, we also study on almost abelian Lie algebras the compatibility between the LCSKT condition and other types of Hermitian structures.

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