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Representation theory depends upon the type of algebraic object being represented. There are several different classes of groups, associative algebras and Lie algebras, and their representation theories all have an individual flavour. Representation theory depends upon the nature of the vector space on which the algebraic object is represented.
In representation theory, the category of representations of some algebraic structure A has the representations of A as objects and equivariant maps as morphisms between them. . One of the basic thrusts of representation theory is to understand the conditions under which this category is semisimple; i.e., whether an object decomposes into simple objects (see Maschke's theorem for the case of ...
This is a glossary of representation theory in mathematics. The term "module" is often used synonymously for a representation; for the module-theoretic terminology, see also glossary of module theory. See also Glossary of Lie groups and Lie algebras, list of representation theory topics and Category:Representation theory.
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures.Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y i conform, in some consistent way, to ...
In representation theory, a subrepresentation of a representation (,) of a group G is a representation (|,) such that W is a vector subspace of V and | = |.. A nonzero finite-dimensional representation always contains a nonzero subrepresentation that is irreducible, the fact seen by induction on dimension.
Veto Players: How Political Institutions Work [1] is a book written by political science professor George Tsebelis in 2002. It is a game theory analysis of political behavior. . In this work Tsebelis uses the concept of the veto player as a tool for analysing the outcomes of political syste
Collective representations are concepts, ideas, categories and beliefs that do not belong to isolated individuals, but are instead the product of a social collectivity. [1] Émile Durkheim (1858-1917) originated the term "collective representations" to emphasise the way that many of the categories of everyday use–space, time, class, number etc–were in fact the product of collective social ...
Therefore, results of the theory of linear representations obtained for the classical complex Lie groups can be carried over to the corresponding compact groups and vice versa. [ 4 ] In terms of Tannakian formalism , Claude Chevalley interpreted Tannaka duality starting from a compact Lie group K as constructing the "complex envelope" G as the ...