Silva Leite, F.; Crouch, P. Closed forms for the exponential mapping on matrix Lie groups based on Putzer’s method. (English) Zbl 0942.22009 J. Math. Phys. 40, No. 7, 3561-3568 (1999). By Putzer’s method closed forms are found for the exponential of the infinitesimal generators of some Lie groups. First, the authors define a class of Lie algebras having a symmetric spectrum. They consider the Lie algebras defined by \( L = \{ A \in Gl (n, \mathbb{R}): A^T P = -PA \} \) and the Jordan algebra defined by \( J = \{ A \in Gl (n, \mathbb{R}): A^T P =PA \} \), where \(P\) is any \(n\times n\) orthogonal matrix. If \(P=I\) and \( L\) and \(J\) are the sets of skew-symmetric and symmetric matrices respectively it is proved that \(P\)-skew symmetric matrices have a symmetric spectrum. Particular cases of \(P\)-skew symmetric matrices are considered. Closed forms are found for the exponential of the infinitesimal generators of the orthogonal group \(SO(2,4)\) and the symplectic group \(SP(3, \mathbb{R})\). Reviewer: Violeta Tretynyk (Kyïv) Cited in 5 Documents MSC: 22E15 General properties and structure of real Lie groups Keywords:Putzer’s method; symmetric matrix; skew-symmetric matrix; symmetric spectrum; exponential PDFBibTeX XMLCite \textit{F. Silva Leite} and \textit{P. Crouch}, J. Math. Phys. 40, No. 7, 3561--3568 (1999; Zbl 0942.22009) Full Text: DOI References: [1] DOI: 10.1137/1020098 · Zbl 0395.65012 · doi:10.1137/1020098 [2] Zeni J., Hadronic J. 13 pp 317– (1990) [3] DOI: 10.1088/0305-4470/27/15/022 · Zbl 0840.22034 · doi:10.1088/0305-4470/27/15/022 [4] DOI: 10.2307/2313914 · Zbl 0135.29801 · doi:10.2307/2313914 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.