Relativity, Supersymmetry, and Strings pp 19-32 | Cite as

# A Quick Introduction to Simple Lie Algebras and Their Representations

## Abstract

Simple Lie algebras, their matrix representations and their subalgebra structure have long been studied by many mathematicians and physicists. Since physicists are interested in the Hilbert space of a quantum-mechanical theory, the traditional approach is to form the generators of a symmetry of a Lagrangian from the fields and then to analyze the symmetry directly in terms of the quantum operators. However, this approach is often cumbersome for dealing with the big groups that appear in string theory. It sometimes helps to proceed somewhat differently, similar to that popular in mathematics. There the focus is on the quantum number labels that appear in the state vectors [1].

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.For reviews of this approach, see, for example, B. 6. Wybourne, Classical Groups for Physicists (Wiley, New Vork, 1974); J. E. Humphreys, Introduction to Lie Algebras and Representation Theory (Springer, New York, 1972);zbMATHCrossRefGoogle Scholar
- 1a.H. Georgi, Lie Algebras in Particle Physics (Benjamin/Cummings, Reading,1982);zbMATHGoogle Scholar
- 1b.R. Slansky, Physics Reports 79 (1981) 1.MathSciNetADSCrossRefGoogle Scholar
- 2.M. R. Bremner, R. V. Moody and J. Patera, Tables of Dominant Weight Multiplicities for Representations of Simple Lie Algebras (Dekker, New York, 1984).Google Scholar
- 3.R. V. Moody and J. Patera, Bull. Am. Math. Soc, 7 (1982) 237.MathSciNetzbMATHCrossRefGoogle Scholar