completely reducible module

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• Module (mathematics) — For other uses, see Module (disambiguation). In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, wherein the corresponding scalars are allowed to lie in an arbitrary ring. Modules also… …   Wikipedia

• Semisimple module — In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring which is a semisimple module over… …   Wikipedia

• Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …   Wikipedia

• Modular representation theory — is a branch of mathematics, and that part of representation theory that studies linear representations of finite group G over a field K of positive characteristic. As well as having applications to group theory, modular representations arise… …   Wikipedia

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• Semisimple — This article is about mathematical use. For the philosophical reduction thinking, see Reduction (philosophy). In mathematics, the term semisimple (sometimes completely reducible) is used in a number of related ways, within different subjects. The …   Wikipedia

• Lie algebra representation — Lie groups …   Wikipedia

• Regular representation — In mathematics, and in particular the theory of group representations, the regular representation of a group G is the linear representation afforded by the group action of G on itself. ignificance of the regular representation of a groupTo say… …   Wikipedia

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• Maschke's theorem — In mathematics, Maschke s theorem,[1][2] named after Heinrich Maschke,[3] is a theorem in group representation theory that concerns the decomposition of representations of a finite group into irreducible pieces. If (V, ρ) is a finite… …   Wikipedia

• Unitary representation — In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π( g ) is a unitary operator for every g ∈ G . The general theory is well developed in case G is a locally compact… …   Wikipedia