An Introduction to Lie Group Integrators
by E. Celledoni, H. Marthinsen, B. Owren
Publisher: arXiv 2012
Number of pages: 28
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion of discrete gradient methods is generalised to Lie groups.
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by Peter J. Cameron - Queen Mary and Westfield College
Notes for an M.Sc. course: Fields and vector spaces; Linear and projective groups; Polarities and forms; Symplectic groups; Unitary groups; Orthogonal groups; Klein correspondence and triality; A short bibliography on classical groups.
by F. Bruhat - Tata Institute of Fundamental Research
We consider some heterogeneous topics relating to Lie groups and the general theory of representations of locally compact groups. We have rigidly adhered to the analytic approach in establishing the relations between Lie groups and Lie algebras.
by Alexander Kirillov, Jr. - SUNY at Stony Brook
The book covers the basic contemporary theory of Lie groups and Lie algebras. This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. Written in an informal style.
by N. Reshetikhin, V. Serganova, R. Borcherds - UC Berkeley
From the table of contents: Tangent Lie algebras to Lie groups; Simply Connected Lie Groups; Hopf Algebras; PBW Theorem and Deformations; Lie algebra cohomology; Engel's Theorem and Lie's Theorem; Cartan Criterion, Whitehead and Weyl Theorems; etc.