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- Trivial_representation abstract "In the mathematical field of representation theory, a trivial representation is a representation (V, φ) of a group G on which all elements of G act as the identity mapping of V. A trivial representation of an associative or Lie algebra is a (Lie) algebra representation for which all elements of the algebra act as the zero linear map (endomorphism) which sends every element of V to the zero vector.For any group or Lie algebra, an irreducible trivial representation always exists over any field, and is one-dimensional, hence unique up to isomorphism. The same is true for associative algebras unless one restricts attention to unital algebras and unital representations.Although the trivial representation is constructed in such a way as to make its properties seem tautologous, it is a fundamental object of the theory. A subrepresentation is equivalent to a trivial representation, for example, if it consists of invariant vectors; so that searching for such subrepresentations is the whole topic of invariant theory.The trivial character is the character that takes the value of one for all group elements.".
- Trivial_representation wikiPageID "450573".
- Trivial_representation wikiPageLength "1530".
- Trivial_representation wikiPageOutDegree "19".
- Trivial_representation wikiPageRevisionID "626833068".
- Trivial_representation wikiPageWikiLink Algebra_over_a_field.
- Trivial_representation wikiPageWikiLink Algebra_representation.
- Trivial_representation wikiPageWikiLink Associative_algebra.
- Trivial_representation wikiPageWikiLink Category:Representation_theory.
- Trivial_representation wikiPageWikiLink Character_(mathematics).
- Trivial_representation wikiPageWikiLink Endomorphism.
- Trivial_representation wikiPageWikiLink Field_(mathematics).
- Trivial_representation wikiPageWikiLink Group_(mathematics).
- Trivial_representation wikiPageWikiLink Group_representation.
- Trivial_representation wikiPageWikiLink Identity_function.
- Trivial_representation wikiPageWikiLink Identity_mapping.
- Trivial_representation wikiPageWikiLink Invariant_theory.
- Trivial_representation wikiPageWikiLink Irreducible_representation.
- Trivial_representation wikiPageWikiLink Lie_algebra.
- Trivial_representation wikiPageWikiLink Lie_algebra_representation.
- Trivial_representation wikiPageWikiLink Linear_map.
- Trivial_representation wikiPageWikiLink Mathematics.
- Trivial_representation wikiPageWikiLink Representation_(mathematics).
- Trivial_representation wikiPageWikiLink Representation_theory.
- Trivial_representation wikiPageWikiLink Unital_algebra.
- Trivial_representation wikiPageWikiLink Zero_element.
- Trivial_representation wikiPageWikiLink Zero_vector.
- Trivial_representation wikiPageWikiLinkText "Trivial representation".
- Trivial_representation wikiPageWikiLinkText "trivial representation".
- Trivial_representation wikiPageWikiLinkText "trivial subrepresentation".
- Trivial_representation hasPhotoCollection Trivial_representation.
- Trivial_representation wikiPageUsesTemplate Template:Algebra-stub.
- Trivial_representation wikiPageUsesTemplate Template:Fulton-Harris.
- Trivial_representation wikiPageUsesTemplate Template:Math.
- Trivial_representation subject Category:Representation_theory.
- Trivial_representation hypernym Representation.
- Trivial_representation type Field.
- Trivial_representation comment "In the mathematical field of representation theory, a trivial representation is a representation (V, φ) of a group G on which all elements of G act as the identity mapping of V.".
- Trivial_representation label "Trivial representation".
- Trivial_representation sameAs m.029zfh.
- Trivial_representation sameAs Q7844662.
- Trivial_representation sameAs Q7844662.
- Trivial_representation sameAs 平凡表示.
- Trivial_representation wasDerivedFrom Trivial_representation?oldid=626833068.
- Trivial_representation isPrimaryTopicOf Trivial_representation.