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Tag Archives: schur’s lemma
Polynomials and Representations XXVIII
Starting from this article, we will look at representations of . Now, itself is extremely complicated so we will only focus on representations of particular types. Generally, for any topological group G, we want: to be a continuous homomorphism of groups. Continuous … Continue reading
Simple Modules
We briefly talked about modules over a (possibly noncommutative) ring R. An important aspect of modules is that unlike vector spaces, modules are usually not free, i.e. they don’t have a basis. For example, take the Zmodule given by Z/2Z. [ Recall: a Zmodule is … Continue reading
Posted in Notes
Tagged algebra, associative algebra, division rings, rings, schur's lemma, simple modules
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Quick Guide to Character Theory (II): Main Theory
Reminder: throughout this series, G is a finite group and K is a field. All Kvector spaces are assumed to be finitedimensional 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