Lecture Notes
Lie Groups, Lie Algebras, and Representation Theory
Lecture Notes
Lie Groups and Lie Algebras
Representation Theory
Problem Sets
Lie Groups and Lie Algebras
Representation Theory
References and Further Reading
Click on linked topics to view lecture notes.
Matrix Lie Groups
The Lie Algebra of the Orthogonal Group \(\mathrm{O}(n)\) (\(\mathrm{SO}(n)\))
Orthogonal Group \(\mathrm{O}(n)\) and Symmetry
The Lorentz Group
Lie Brackets (for \(n\times n\) Matrices)
More Examples of Lie Groups: 3-Sphere as a Lie Group, The 3-Dimensional Heisenberg Group
Lie Group and Lie Algebra Representations
Quantum Angular Momentum and \(\mathfrak{su}(2)\) Representation
Quantum Angular Momentum in \(\mathbb{R}^{2+2}\) and \(\mathfrak{su}(1,1)\)
Lie Group Actions and Lie Group Representations
Irreducible Representations of \(\mathrm{U}(1)\)
The Representation of \(\mathrm{SU}(2)\)
Click on the following links for problems.
Michael F. Atiyah, R. Bott, S. Helgason, D. Kazhdan, B. Kostant, G. Lusztig, I.G. Macdonald, G.W. Mackey, W. Schmid and D.J. Simms, Representation Theory of Lie Groups, Proceedings of the SRC/LMS Research Symposium on Representations of Lie Groups, Oxford, 28 June-15 July 1977, Cambridge University Press, 1979
John Baez and Javier P. Muniain, Gauge Fields, Knots and Gravity, World Scientific, 1994
Andrew Baker, Matrix Groups, An Introduction to Lie Group Theory, Springer_verlag, 2001
Robert L. Bryant, An Introduction to Lie Groups and Symplectic Geometry, A series of nine lectures on Lie groups and symplectic geometry delivered at the Regional Geometry Institute in Park City, Utah, 24 Junes-20 July 1991
Robert N. Cahn, Semi-Simple Lie Algebras and Their Representations, Benjamin-Cummings, 1984
Brian C. Hall, An Elementary Introduction to Groups and Representations
Brian C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Graduate Texts in Mathematics, v. 222, Corr. 2nd Printing, Springer, 2004
James E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, 1972
H. F. Jones, Groups, Representations and Physics, Institute of Physics Publishing, 1998
Dong Hoon Lee, The structure of complex Lie groups, Chapman & Hall/CRC, 2002
Barry Simon, Representations of Finite and Compact Groups, American Mathematical Society, 1996
Shlomo Sternberg, Group Theory and Physics, Cambridge University Press, 1994
Peter Woit, Quantum Theory, Groups and Representations: An Introduction