New Parameterizations of \(\mathrm{SL}(2,\mathbb{R})\) and Some Explicit Formulas for Its Logarithm
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Published:2021
Issue:
Volume:60
Page:65-81
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ISSN:1312-5192
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Container-title:Journal of Geometry and Symmetry in Physics
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language:
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Short-container-title:J Geom Symmetry Phys
Author:
Valchev Tihomir, ,Mladenova Clementina,Mladenov Ivaïlo
Abstract
Here we demonstrate some of the benefits of a novel parameterization of the Lie groups $\mathrm{Sp}(2,\bbr)\cong\mathrm{SL}(2,\bbr)$. Relying on the properties of the exponential map $\mathfrak{sl}(2,\bbr)\to\mathrm{SL}(2,\bbr)$, we have found a few explicit formulas for the logarithm of the matrices in these groups.\\ Additionally, the explicit analytic description of the ellipse representing their field of values is derived and this allows a direct graphical identification of various types.
Publisher
Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)
Subject
Geometry and Topology,Mathematical Physics