Lie group

English Etymology Named for Norwegian mathematician Sophus Lie. Noun en topology Any group that is a smooth manifold and whose group operations are differentiable. 1994, Silvio Levy (translator), Albert S. Schwarz, Topology for Physicists, [1989, A. S. Shvarts, Kvantovaya teoriya polya i topologiya], Springer, 1996, 2nd Printing, page 233, Every connected Lie group is homotopically equivalent to its maximal compact subgroup. This reduces the study of the homotopy and homology of Lie groups to the compact case. en 2009 Mikio Nakahara Geometry, Topology and Physics 2nd https://books.google.com.au/books?id=cH-XQB0Ex5wC&pg=PA207&dq=%22Lie+group%22%7C%22Lie+groups%22+-intitle:lie&hl=en&sa=X&ved=0ahUKEwiK1YuOz97WAhWBzbwKHW8PAVMQ6AEIfTAP#v=onepage&q=%22Lie%20group%22%7C%22Lie%20groups%22%20-intitle%3Alie&f=false 207 Taylor & Francis A Lie group is a manifold on which the group manipulations, product and inverse, arc defined. Lie groups play an extremely important role in the theory of fibre bundles and also find vast applications in physics. en 2009 Boris Khesin; Robert Wendt The Geometry of Infinite-Dimensional Groups https://books.google.com.au/books?id=xZvLBvqN8fsC&pg=PA1&dq=%22Lie+group%22%7C%22Lie+groups%22+-intitle:lie&hl=en&sa=X&ved=0ahUKEwiK1YuOz97WAhWBzbwKHW8PAVMQ6AEIdjAO#v=onepage&q=%22Lie%20group%22%7C%22Lie%20groups%22%20-intitle%3Alie&f=false 1 Springer As is well known, in finite dimensions each Lie group is, at least locally near the identity, completely described by its Lie algebra. Hypernyms en topological group Hyponyms en circle group en Möbius group Related terms en group of Lie type en Lie algebra Translations analytic group that is also a smooth manifold Danish: da Liegruppe c Finnish: fi Lien ryhmä French: fr groupe de Lie m German: de Lie-Gruppe f, de Liesche Gruppe f Italian: it gruppo di Lie m Japanese: ja リー群 rīgun Polish: pl grupa Liego f Russian: ru группа Ли f Spanish: es grupo de Lie m Further reading Lie theory en Manifolds en eponyms