Simple Lie Group: Mathematics, Normal Subgroups, Connected Space, Semisimple Lie algebra - Tapa blanda

Simple Lie Group

Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In mathematics, asimple Lie group is a connected non-abelian Lie group G which does nothave nontrivial connected normal subgroups. A simple Lie algebra is anon-abelian Lie algebra whose only ideals are 0 and itself. A direct sumof simple Lie algebras is called a semisimple Lie algebra. An equivalentdefinition of a simple Lie group follows from the Lie correspondence: aconnected Lie group is simple if its Lie algebra is simple. An importanttechnical point is that a simple Lie group may contain discrete normalsubgroups, hence being a simple Lie group is different from being simpleas an abstract group. Simple Lie groups include many classical Liegroups, which provide a group-theoretic underpinning for sphericalgeometry, projective geometry and related geometries in the sense ofFelix Klein's Erlangen programme. It emerged in the course ofclassification of simple Lie groups that there exist also severalexceptional possibilities not corresponding to any familiar geometry.These exceptional groups account for many special examples andconfigurations in other branches of mathematics, as well as contemporarytheoretical physics.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 84 pp. Englisch. Nº de ref. del artículo: 9786130579920

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