Monthly Archives: January 2015

The Group Algebra (III)

As alluded to at the end of the previous article, we shall consider the case where K is algebraically closed, i.e. every polynomial with coefficients in K factors as a product of linear polynomials. E.g. K = C is a common choice. Having assumed … Continue reading

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The Group Algebra (II)

We continue our discussion of the group algebra. Constructing K[G]-modules Recall that such a module V is also called a representation of G over K, and corresponds to a group homomorphism (i) Given a K[G]-module V, a submodule W of V is precisely a vector subspace W such that g(W) ⊆ W for … Continue reading

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The Group Algebra (I)

[ Note: the contents of this article overlap with a previous series on character theory. ] Let K be a field and G a finite group. The group algebra K[G] is defined to be a vector space over K with basis , where “g” here is … Continue reading

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