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 J. S. Milne
This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. Algebraic groups are groups defined by polynomials. Those in this book can all be realized as groups of matrices.
by John Edward Campbell - Oxford Clarendon Press
In this treatise an attempt is made to give, in as elementary a form as possible, the main outlines of Lie's theory of Continuous Groups. Even those familiar with the theory may find something new in the form in which the theory is here presented.
by Jean Gallier - University of Pennsylvania
Contents: Introduction to Manifolds and Lie Groups; Review of Groups and Group Actions; Manifolds; Construction of Manifolds From Gluing Data; Lie Groups, Lie Algebra, Exponential Map; The Derivative of exp and Dynkin's Formula; etc.
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.