About: Complex reflection group

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In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise.

Attributes	Values
rdf:type	yago:WikicatLieGroups yago:Abstraction100002137 yago:Group100031264 Band
rdfs:label	Complex reflection group (en) Группа комплексных отражений (ru)
rdfs:comment	Группа комплексных отражений — конечная группа, действующая на конечномерном комплексном векторном пространстве определённым образом. (ru) In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise. (en)
dcterms:subject	Group theory Geometry Reflection groups
Wikipage page ID	5381096 (xsd:integer)
Wikipage revision ID	1105297161 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Binary tetrahedral group Hyperoctahedral group Vector space Index of a subgroup Inventiones Mathematicae Group theory Complex numbers Coxeter Mathematics Chevalley–Shephard–Todd theorem Generalized symmetric group Monomial matrices Roots of unity Geometry American Mathematical Society Cyclic group Central product Regular polyhedron Wreath product Group (mathematics) Invariant theory Coxeter group Hyperplane Reflection groups Binary icosahedral group Binary octahedral group Hessian group Mitchell's group Dihedral group Polynomial ring Klein quartic Cartan matrix Semidirect product Klein four-group Valentiner group Extra special group Symmetric group Weyl group Finite-dimensional vector space Coxeter number Journal für die reine und angewandte Mathematik Regular complex polytope Primitive root of unity
Link from a Wikipage to an external page	http://magma.maths.usyd.edu.au/magma/htmlhelp/text1038.htm https://www.math.ucla.edu/~rouquier/papers/banff.pdf https://books.google.com/books%3Fid=Bi7EKLHppuYC http://citeseer.ist.psu.edu/cache/papers/cs/14118/http:zSzzSzwww.math.jussieu.frzSz~rouquierzSzpreprintszSzbrmaro.pdf/complex-reflection-groups-braid.pdf
sameAs	Complex reflection group Complex reflection group Complex reflection group Complex reflection group Complex reflection group
dbp:wikiPageUsesTemplate	dbt:= dbt:CDD dbt:Citation dbt:Clarify dbt:ISBN dbt:Math dbt:Reflist dbt:Su dbt:Harvs
mr	1637497 (xsd:integer)
b	6 (xsd:integer) 8 (xsd:integer)
first	Michel (en) Gunter (en) J. A. (en) G. C. (en) Raphaël (en)
ISSN	75 (xsd:integer)
last	Malle (en) Todd (en) Shephard (en) Broué (en) Rouquier (en)
p	+ (en) − (en)
pages	127 (xsd:integer)
title	Complex reflection groups, braid groups, Hecke algebras (en)
url	http://citeseer.ist.psu.edu/cache/papers/cs/14118/http:zSzzSzwww.math.jussieu.frzSz~rouquierzSzpreprintszSzbrmaro.pdf/complex-reflection-groups-braid.pdf
volume	500 (xsd:integer)
year	1954 (xsd:integer) 1998 (xsd:integer)
has abstract	In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise. Complex reflection groups arise in the study of the invariant theory of polynomial rings. In the mid-20th century, they were completely classified in work of Shephard and Todd. Special cases include the symmetric group of permutations, the dihedral groups, and more generally all finite real reflection groups (the Coxeter groups or Weyl groups, including the symmetry groups of regular polyhedra). (en) Группа комплексных отражений — конечная группа, действующая на конечномерном комплексном векторном пространстве определённым образом. (ru)
author1-link	Geoffrey Colin Shephard (en)

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