Baker–Campbell–Hausdorff–Dynkin Formula for the Lie Algebra of Rigid Body Displacements

Daniel Condurache and Ioan-Adrian Ciureanu
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Daniel Condurache: Technical University of Iasi, D. Mangeron 59, 700050 Iasi, Romania
Ioan-Adrian Ciureanu: “Grigore T. Popa” University of Medicine and Pharmacy Iasi, 700116 Iasi, Romania

Mathematics, 2020, vol. 8, issue 7, 1-19

Abstract: The paper proposes, for the first time, a closed form of the Baker–Campbell–Hausdorff–Dynkin (BCHD) formula in the particular case of the Lie algebra of rigid body displacements. For this purpose, the structure of the Lie group of the rigid body displacements S E ( 3 ) and the properties of its Lie algebra s e ( 3 ) are used. In addition, a new solution to this problem in dual Lie algebra of dual vectors is delivered using the isomorphism between the Lie group S E ( 3 ) and the Lie group of the orthogonal dual tensors.

Keywords: BCHD formula; Lie group; Lie algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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