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Monthly Archives: May 2013
Quick Guide to Character Theory (II): Main Theory
Reminder: throughout this series, G is a finite group and K is a field. All K-vector spaces are assumed to be finite-dimensional over K. G4. Maschke’s Theorem If is a K[G]-submodule, it turns out V is isomorphic to the direct sum of W and some other submodule W’. … Continue reading
Quick Guide to Character Theory (I): Foundation
Character theory is one of the most beautiful topics in undergraduate mathematics; the objective is to study the structure of a finite group G by letting it act on vector spaces. Earlier, we had already seen some interesting results (e.g. proof … Continue reading
Posted in Notes
Tagged character theory, dual spaces, fields, group algebras, groups, modules, representation theory
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Mathematics and Such 