From DK-STP to a set of Lie bracket

Qi Qi; Jun-e Feng; Qi Qi; Jun-e Feng

doi:10.3934/mmc.2025029

Mathematical Modelling and Control

2025, Volume 5, Issue 4: 410-420. doi: 10.3934/mmc.2025029

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Research article

From DK-STP to a set of Lie bracket

Qi Qi ,
Jun-e Feng ^,

School of Mathematics, Shandong University, Jinan 250100, China

Received: 06 November 2024 Revised: 10 December 2024 Accepted: 09 January 2025 Published: 04 December 2025

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.
- semi-tensor product,
- dimension keeping semi-tensor product,
- (anti) commutativity,
- Lie bracket,
- structure matrix
Citation: Qi Qi, Jun-e Feng. From DK-STP to a set of Lie bracket[J]. Mathematical Modelling and Control, 2025, 5(4): 410-420. doi: 10.3934/mmc.2025029

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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.

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