22C05 Compact groups

Overview

22C05 studies compact groups in compact groups. It studies compact topological groups and the harmonic analysis, representation theory, and measure-theoretic structure they support.

Related Wikipedia Page

Compact Groups (Wikipedia)

Useful Links

• Compact Groups (Wikipedia)
• Compact group (Wikipedia)
• Haar measure (Wikipedia)

Key Ideas

• Canonical formulations and representative examples for compact groups
• How structural, local, and computational viewpoints interact in the subject
• Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to analyze Haar measure, representations, and structural decomposition in compact symmetry groups.

Applications

• Harmonic analysis on compact groups
• Representation theory
• Invariant measures and averaging

References

• Folland, G.B. (2016) A Course in Abstract Harmonic Analysis. 2nd edn. Boca Raton, FL: CRC Press.
• Pontryagin, L.S. (1986) Topological Groups. 3rd edn. New York, NY: Gordon and Breach.

Recommended Textbooks

• Morris, S.A. (2013) Pontryagin Duality and the Structure of Locally Compact Abelian Groups. Cambridge: Cambridge University Press.
• Hewitt, E. and Ross, K.A. (1970) Abstract Harmonic Analysis. Vol. 1. New York, NY: Springer.