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- Affine_representation abstract "An affine representation of a topological (Lie) group G on an affine space A is a continuous (smooth) group homomorphism from G to the automorphism group of A, the affine group Aff(A). Similarly, an affine representation of a Lie algebra g on A is a Lie algebra homomorphism from g to the Lie algebra aff(A) of the affine group of A.An example is the action of the Euclidean group E(n) upon the Euclidean space En.Since the affine group in dimension n is a matrix group in dimension n + 1, an affine representation may be thought of as a particular kind of linear representation. We may ask whether a given affine representation has a fixed point in the given affine space A. If it does, we may take that as origin and regard A as a vector space: in that case, we actually have a linear representation in dimension n. This reduction depends on a group cohomology question, in general.".
- Affine_representation wikiPageID "354593".
- Affine_representation wikiPageLength "1638".
- Affine_representation wikiPageOutDegree "21".
- Affine_representation wikiPageRevisionID "649712578".
- Affine_representation wikiPageWikiLink Affine_group.
- Affine_representation wikiPageWikiLink Affine_space.
- Affine_representation wikiPageWikiLink Automorphism.
- Affine_representation wikiPageWikiLink Category:Homological_algebra.
- Affine_representation wikiPageWikiLink Category:Representation_theory_of_Lie_algebras.
- Affine_representation wikiPageWikiLink Category:Representation_theory_of_Lie_groups.
- Affine_representation wikiPageWikiLink Continuous_function.
- Affine_representation wikiPageWikiLink Euclidean_group.
- Affine_representation wikiPageWikiLink Euclidean_space.
- Affine_representation wikiPageWikiLink Fixed_point_(mathematics).
- Affine_representation wikiPageWikiLink Group_action.
- Affine_representation wikiPageWikiLink Group_cohomology.
- Affine_representation wikiPageWikiLink Group_homomorphism.
- Affine_representation wikiPageWikiLink Lie_algebra.
- Affine_representation wikiPageWikiLink Lie_group.
- Affine_representation wikiPageWikiLink Projective_representation.
- Affine_representation wikiPageWikiLink Representation_theory.
- Affine_representation wikiPageWikiLink Smoothness.
- Affine_representation wikiPageWikiLink Topological_group.
- Affine_representation wikiPageWikiLink Vector_space.
- Affine_representation wikiPageWikiLinkText "Affine representation".
- Affine_representation wikiPageWikiLinkText "affine representation".
- Affine_representation wikiPageUsesTemplate Template:Algebra-stub.
- Affine_representation wikiPageUsesTemplate Template:Citation.
- Affine_representation subject Category:Homological_algebra.
- Affine_representation subject Category:Representation_theory_of_Lie_algebras.
- Affine_representation subject Category:Representation_theory_of_Lie_groups.
- Affine_representation hypernym Homomorphism.
- Affine_representation type Algebra.
- Affine_representation type Field.
- Affine_representation comment "An affine representation of a topological (Lie) group G on an affine space A is a continuous (smooth) group homomorphism from G to the automorphism group of A, the affine group Aff(A).".
- Affine_representation label "Affine representation".
- Affine_representation sameAs Q3892887.
- Affine_representation sameAs Afina_prezento.
- Affine_representation sameAs Representação_afim.
- Affine_representation sameAs m.01zqch.
- Affine_representation sameAs Q3892887.
- Affine_representation wasDerivedFrom Affine_representation?oldid=649712578.
- Affine_representation isPrimaryTopicOf Affine_representation.