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April 1, 2026

The classification of Hermitian and hyper-Hermitian structures on Lie groups with one-dimensional commutator groups

Key Points

This work aims to classify left-invariant Hermitian and hyper-Hermitian structures on certain Lie groups.
Classified left-invariant structures on Lie groups with one-dimensional commutator groups.
Constructed n-dimensional Lie groups with specified structures for natural numbers n = 2k and n = 4k.
All left-invariant Hermitian and hyper-Hermitian structures on the specified Lie groups are classified.
Examples of n-dimensional Lie groups with one-dimensional commutator groups possessing the desired structures are provided.

Abstract

This paper classifies all left-invariant Hermitian and hyper-Hermitian structures on Lie groups whose commutator groups are one-dimensional. Furthermore, for each natural number n = 2k and n = 4k (k > 1 for the case of hyper-Hermitian structures), we construct an n-dimensional Lie group with a one-dimensional commutator group that possesses left-invariant Hermitian and hyper-Hermitian structures, respectively.

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The classification of Hermitian and hyper-Hermitian structures on Lie groups with one-dimensional commutator groups

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