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Research Article | Open Access

From DK-STP to a set of Lie bracket

Qi Qi, Jun-e Feng( )
School of Mathematics, Shandong University, Jinan 250100, China
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Abstract

In this paper, semi-tensor product (STP) and related properties of dimension keeping semi-tensor product (DK-STP) are analyzed. The commutativity and anticommutativity of DK-STP are studied by means of matrix mapping, and sufficient conditions for both are obtained. The structure matrix of the Lie bracket of non-square matrices (NSM) is discussed, and some properties are derived. The correspondences between the special Lie subalgebras of square matrix and Lie subalgebras of NSM are discussed through a homomorphism.

Keywords

semi-tensor productdimension keeping semi-tensor product(anti) commutativityLie bracketstructure matrix

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Mathematical Modelling and Control
Volume 5 Issue 4,
December 2025
Pages 410-420
DOI: 10.3934/mmc.2025029

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Qi Q, Feng J-e. From DK-STP to a set of Lie bracket. Mathematical Modelling and Control, 2025, 5(4): 410-420. https://doi.org/10.3934/mmc.2025029

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Received: 06 November 2024
Revised: 10 December 2024
Accepted: 09 January 2025
Published: 15 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)