Introduction to lie algebras

Includes bibliography and index

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.

https://link.springer.com/book/10.1007/1-84628-490-2#:~:text=Introduction%20to%20Lie%20Algebras%20covers,in%20mathematics%20and%20theoretical%20physics.