|Lie triple systems have natural embeddings into certain canonical Lie algebras, the so-called Â“standardÂ” and Â“universalÂ” embeddings, and any Lie triple system can be shown to arise precisely as the −1-eigenspace of an involution (an automorphism which squares to the identity) on some Lie algebra.
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature and their tangents. This theory can be used to unify a range of different topics, such as polar-type matrix decompositions, splitting methods for computation of the matrix exponential, composition of self adjoint numerical integrators and dynamical systems with symmetries and reversing symmetries.
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