| Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA252.3.SPR. FCT 94825 (Browse shelf) | 1 | Available |
Browsing Biblioteca da FCTUNL Shelves , Shelving location: Online , Collection code: Não Ficção Close shelf browser
| QA805.SPR. FCT 94820 Mathematical aspects of classical and celestial mechanics | QA274.2.SPR. FCT 94823 From stochastic calculus to mathematical finance | QA169.SPR. FCT 94824 Categories and sheaves | QA252.3.SPR. FCT 94825 Introduction to Lie algebras | QA10.7.SPR. FCT 94827 Matematica e cultura 2006 | QA299.3.SPR. FCT 94831 Geometric numerical integration | QA274.2.SPR. FCT 94832 In memoriam Paul-André Meyer |
Colocação: Online
Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. Based on a lecture course given to fourth-year undergraduates, this book provides an elementary introduction to Lie algebras. It starts with basic concepts. A section on low-dimensional Lie algebras provides readers with experience of some useful examples. This is followed by a discussion of solvable Lie algebras and a strategy towards a classification of finite-dimensional complex Lie algebras. The next chapters cover Engel's theorem, Lie's theorem and Cartan's criteria and introduce some representation theory. The root-space decomposition of a semisimple Lie algebra is discussed, and the classical Lie algebras studied in detail. The authors also classify root systems, and give an outline of Serre's construction of complex semisimple Lie algebras. An overview of further directions then concludes the book and shows the high degree to which Lie algebras influence present-day mathematics. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.
There are no comments for this item.