nLab Tannaka-Krein theorem

Idea

The Tannaka-Krein theorem (in the narrow sense) is a particular Tannaka duality theorem for compact topological groups.

References

The original theorem is (in two independent and different formulations) stated and proved in

• Tadao Tannaka: Über den Dualitätssatz der nichtkommutativen topologischen Gruppen, Tohoku Math. J. 45 1 (1938) 1-12

• Mark G. Krein: A principle of duality for bicompact groups and quadratic block algebras, Doklady AN SSSR 69 (1949) 725-728

Textbook account:

• E. Hewitt, K. A. Ross, Abstract harmonic analysis, 2 vols.

See also

• Alexander Rosenberg, Reconstruction of groups , Selecta Math. N.S. 9 1 (2003)