INTRODUCTION TO LIE ALGEBRAS KARIN ERDMANN PDF

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 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. 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 root-space decomposition of a semisimple Lie algebra is discussed, and the classical Lie algebras studied in detail.

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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 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.

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 root-space decomposition of a semisimple Lie algebra is discussed, and the classical Lie algebras studied in detail.

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.

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Introduction to Lie Algebras

It is based on 4th year courses given by the authors in Oxford. As such, it is particularly aimed at 3rd and 4th year undergraduates, but we hope it will be useful to anyone who wants a gentle introduction to the subject. The approach is very elementary. The only prerequisite knowledge needed is some linear algebra, most of which is summarised in an appendix. Numerous examples are given, including a classification of all 3-dimensional complex Lie algebras. The root space decompositions of the classical Lie algebras are worked out in detail.

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Mark Wildon's Website: Introduction to Lie algebras

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