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System of imprimitivity

The concept of a system of imprimitivity is used in mathematics, particularly in algebra and analysis, both within the context of the theory of group representations. It was used by George Mackey as the basis for his theory of induced unitary representations of locally compact groups.

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Example

Infinite dimensional systems of imprimitivity

Homogeneous systems of imprimitivity

Induced representations

Applications to the theory of group representations

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System of imprimitivity

Nodes53
Edges52
Triples18
Avg. degree1.96
Density0.037736
Components1

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System of imprimitivity

Top relations

related to Homogeneous systems of imprimitivity · 6
System of imprimitivity → Any, Borel, In, It, Lemma, Xn
related to Infinite dimensional systems of imprimitivity · 6
System of imprimitivity → As, Borel, L2, Mackey's, The, To
related to Example · 5
System of imprimitivity → Borel, Hilbert, If, Moreover, Ug
is a · 1
System of imprimitivity → orthogonal direct sum of homogeneous ones.It can be shown that if the action of G on X is transitive

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Important terminology

imprimitivity representation group system borel representations action measure unitary space case theory homogeneous subgroup induced finite groups example sets corresponding

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SubjectPredicateObjectConfidenceSrc
System of imprimitivityis aorthogonal direct sum of homogeneous ones.It can be shown that if the action of G on X is transitive0.90text
System of imprimitivityrelated to ExampleHilbert0.60section
System of imprimitivityrelated to ExampleUg0.60section
System of imprimitivityrelated to ExampleBorel0.60section
System of imprimitivityrelated to ExampleIf0.60section
System of imprimitivityrelated to ExampleMoreover0.60section
System of imprimitivityrelated to Homogeneous systems of imprimitivityIn0.60section
System of imprimitivityrelated to Homogeneous systems of imprimitivityXn0.60section
System of imprimitivityrelated to Homogeneous systems of imprimitivityBorel0.60section
System of imprimitivityrelated to Homogeneous systems of imprimitivityIt0.60section
System of imprimitivityrelated to Homogeneous systems of imprimitivityLemma0.60section
System of imprimitivityrelated to Homogeneous systems of imprimitivityAny0.60section

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