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Lie Groups and Lie Algebras
This course introduces the theory of Lie groups and Lie algebras, exploring their rich structure and applications in mathematics and physics. Topics include the classification of Lie algebras, the geometry of Lie groups, and the theory of fibre bundles. The course will culminate in applications such as gauge theory, Yang-Mills fields, and symmetries in physics.
1. Define and provide examples of Lie groups and Lie algebras.2. Explain the relationship between Lie groups and their corresponding Lie algebras.3. Use the exponential map and discuss its role in connecting Lie algebras to Lie groups.4. Classify Lie algebras using root systems and Dynkin diagrams.5. Analyze representations of Lie algebras and their role in both mathematics and physics.6. Understand the geometric framework of principal and associated fibre bundles.7. Apply connections, curvature, and parallel transport to problems in physics.8. Discuss advanced applications such as Yang-Mills theory, quantum mechanics, and symmetries in physical systems.with 7. and 8. based on the interest of the class.
Subject to approval of the Head of School.
Students must attend one activity from each section.
Chris Stevens
Library portalLearn Postgraduate
Domestic fee $1,138.00
International Postgraduate fees
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see Mathematics and Statistics .