The Lie Algebra $\mathfrak{sl}(2,\mathbb{R})$ and Noether Point Symmetries of Lagrangian Systems

Campoamor-Stursberg, Rutwig

doi:10.7546/giq-20-2019-99-114

VOL. 20 | 2019 The Lie Algebra $\mathfrak{sl}(2,\mathbb{R})$ and Noether Point Symmetries of Lagrangian Systems

Chapter Author(s) Rutwig Campoamor-Stursberg

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Geom. Integrability & Quantization, 2019: 99-114 (2019) DOI: 10.7546/giq-20-2019-99-114

Abstract

Some aspects of the simple Lie algebra $\mathfrak{sl}(2,\mathbb{R})$ realized as a subalgebra of Noether point symmetries of Lagrangian systems and related inverse problems are discussed, specially in connection to Lagrangians of kinetic type and some geometric properties like sectional curvatures.