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April 1, 2026International Journal of Mathematics0 citations

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

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HMHamid Reza Salimi Moghaddam

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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Hamid Reza Salimi Moghaddam (2026) studied this question.

synapsesocial.com/papers/69ccb76c16edfba7beb89585https://doi.org/10.1142/s0129167x26420012
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