|A Lie triple system is a subspace of a Lie algebra closed under the ternary composition [[xy]z]; equivalently, it may be defined as the subspace of elements mapped into their negatives by an automorphism of order two in a Lie algebra; or, finally, a Lie triple system may be defined by a set of identities. 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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