Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Bracket_ring> ?p ?o. }
Showing items 1 to 14 of
14
with 100 items per page.
- Bracket_ring abstract "In mathematics, the bracket ring is the subring of the ring of polynomials k[x11,...,xdn] generated by the d by d minors of a generic d by n matrix (xij).The bracket ring may be regarded as the ring of polynomials on the image of a Grassmannian under the Plücker embedding.For given d ≤ n we define as formal variables the brackets [λ1 λ2 ... λd] with the λ taken from {1,...,n}, subject to [λ1 λ2 ... λd] = − [λ2 λ1 ... λd] and similarly for other transpositions. The set Λ(n,d) of size generates a polynomial ring K[Λ(n,d)] over a field K. There is a homomorphism Φ(n,d) from K[Λ(n,d)] to the polynomial ring K[xi,j] in nd indeterminates given by mapping [λ1 λ2 ... λd] to the determinant of the d by d matrix consisting of the columns of the xi,j indexed by the λ. The bracket ring B(n,d) is the image of Φ. The kernel I(n,d) of Φ encodes the relations or syzygies that exist between the minors of a generic n by d matrix. The projective variety defined by the ideal I is the (n−d)d dimensional Grassmann variety whose points correspond to d-dimensional subspaces of an n-dimensional space.To compute with brackets it is necessary to determine when an expression lies in the ideal I(n,d). This is achieved by a straightening law due to Young (1928).".
- Bracket_ring wikiPageExternalLink stanley1.ps.
- Bracket_ring wikiPageID "35215473".
- Bracket_ring wikiPageRevisionID "580066973".
- Bracket_ring hasPhotoCollection Bracket_ring.
- Bracket_ring subject Category:Algebraic_geometry.
- Bracket_ring subject Category:Invariant_theory.
- Bracket_ring comment "In mathematics, the bracket ring is the subring of the ring of polynomials k[x11,...,xdn] generated by the d by d minors of a generic d by n matrix (xij).The bracket ring may be regarded as the ring of polynomials on the image of a Grassmannian under the Plücker embedding.For given d ≤ n we define as formal variables the brackets [λ1 λ2 ... λd] with the λ taken from {1,...,n}, subject to [λ1 λ2 ... λd] = − [λ2 λ1 ... λd] and similarly for other transpositions.".
- Bracket_ring label "Bracket ring".
- Bracket_ring sameAs m.0j7lsr8.
- Bracket_ring sameAs Q4953691.
- Bracket_ring sameAs Q4953691.
- Bracket_ring wasDerivedFrom Bracket_ring?oldid=580066973.
- Bracket_ring isPrimaryTopicOf Bracket_ring.