Monomial representation (original) (raw)
In the mathematical fields of representation theory and group theory, a linear representation ρ (rho) of a group G is a monomial representation if there is a finite-index subgroup H and a one-dimensional linear representation σ of H, such that ρ is equivalent to the induced representation IndHGσ. Alternatively, one may define it as a representation whose image is in the monomial matrices.
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| dbo:abstract | In the mathematical fields of representation theory and group theory, a linear representation ρ (rho) of a group G is a monomial representation if there is a finite-index subgroup H and a one-dimensional linear representation σ of H, such that ρ is equivalent to the induced representation IndHGσ. Alternatively, one may define it as a representation whose image is in the monomial matrices. Here for example G and H may be finite groups, so that induced representation has a classical sense. The monomial representation is only a little more complicated than the permutation representation of G on the cosets of H. It is necessary only to keep track of scalars coming from σ applied to elements of H. (en) In matematica, una rappresentazione lineare del gruppo G è una rappresentazione monomiale ed è presente l'indice del sottogruppo H e la rappresentazione linerare di H, rendendo la rappresentazione analoga alla . Alternativamente, qualcuno potrebbe definire tale definizione come rappresentazione dell'immagine presente nella . Per esempio G e H sono gruppi finiti, quindi la rappresentazione indotta evince un senso classico. La rappresentazione monomiale è solo un minimo più complicata della di G sulla classe laterale di H. È necessario solamente mantenere traccia degli scalari provenienti dagli elemenenti applicati di H. (it) |
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| dbo:wikiPageWikiLink | dbr:Scalar_(mathematics) dbr:Representation_theory dbr:Coset dbr:Monomial_matrices dbr:Permutation_representation dbr:Subgroup dbr:Rho dbr:Group_(mathematics) dbc:Representation_theory_of_groups dbr:Group_theory dbr:Induced_representation dbr:Image_(mathematics) dbr:Finite_group dbr:Mathematical dbr:Linear_representation |
| dbp:id | Monomial_representation (en) |
| dbp:title | Monomial representation (en) |
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| dcterms:subject | dbc:Representation_theory_of_groups |
| gold:hypernym | dbr:Representation |
| rdfs:comment | In the mathematical fields of representation theory and group theory, a linear representation ρ (rho) of a group G is a monomial representation if there is a finite-index subgroup H and a one-dimensional linear representation σ of H, such that ρ is equivalent to the induced representation IndHGσ. Alternatively, one may define it as a representation whose image is in the monomial matrices. (en) In matematica, una rappresentazione lineare del gruppo G è una rappresentazione monomiale ed è presente l'indice del sottogruppo H e la rappresentazione linerare di H, rendendo la rappresentazione analoga alla . Alternativamente, qualcuno potrebbe definire tale definizione come rappresentazione dell'immagine presente nella . (it) |
| rdfs:label | Rappresentazione monomiale (it) Monomial representation (en) |
| owl:sameAs | freebase:Monomial representation wikidata:Monomial representation dbpedia-it:Monomial representation https://global.dbpedia.org/id/3e8PT |
| prov:wasDerivedFrom | wikipedia-en:Monomial_representation?oldid=1094901198&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Monomial_representation |
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