# On left-invariant semi-K\\"{a}hler structures on six-dimensional nilpotent nonsymplectic Lie groups

Source: [On left-invariant semi-K\\"{a}hler structures on six-dimensional nilpotent nonsymplectic Lie groups](<https://www.sota2.com/research/paper/68fa5c421e209131ce9cf3eb>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:31:28.881Z

Authors: N. K. Smolentsev, K. V. Chernova

Published: 2024-08-27T02:00:12.000Z

## Abstract

It is known that there are 34 classes of six-dimensional nilpotent Lie groups, many of which admit left-invariant symplectic and complex structures. Among them there are three classes of groups on which there are no left-invariant symplectic structures, but there are complex structures. In this work, semi-K\\"{a}hler and almost para-semi-K\\"{a}hler structures are defined on such Lie groups and their geometric properties are studied.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2408.14733>)

[PDF](<https://arxiv.org/pdf/2408.14733.pdf>)