|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.
Open access to the scientific literature means the removal of barriers (including price barriers) from accessing scholarly work. There are two parallel roadsÂť towards open access: Open Access articles and self-archiving. Open Access articles are immediately, freely available on their Web site, a model mostly funded by charges paid by the author (usually through a research grant). The alternative for a researcher is self-archivingÂť (i.e., to publish in a traditional journal, where only subscribers have immediate access, but to make the article available on their personal and/or institutional Web sites (including so-called repositories or archives)), which is a practice allowed by many scholarly journals. Open Access raises practical and policy questions for scholars, publishers, funders, and policymakers alike, including what the return on investment is when paying an article processing fee to publish in an Open Access articles, or whether investments into institutional repositories should be made and whether self-archiving should be made mandatory, as contemplated by some funders.