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024 7 $a10.1007/978-3-642-11175-4
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035   $a(DE-He213)978-3-642-11175-4
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100   $a20100301d2010      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aIntroduction to Complex Reflection Groups and Their Braid Groups$b[electronic resource] /$fby Michel Broué
205   $a1st ed. 2010.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2010.
215   $a1 online resource (XII, 144 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1988
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-11174-2 
311   $a3-642-11184-X 
320   $aIncludes bibliographical references and index.
327   $aPreliminaries -- Prerequisites and Complements in Commutative Algebra -- Polynomial Invariants of Finite Linear Groups -- Finite Reflection Groups in Characteristic Zero -- Eigenspaces and Regular Elements.
330   $aWeyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra. It has recently been discovered that complex reflection groups play a key role in the theory of finite reductive groups, giving rise as they do to braid groups and generalized Hecke algebras which govern the representation theory of finite reductive groups. It is now also broadly agreed upon that many of the known properties of Weyl groups can be generalized to complex reflection groups. The purpose of this work is to present a fairly extensive treatment of many basic properties of complex reflection groups (characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, etc.) including the basic findings of Springer theory on eigenspaces. In doing so, we also introduce basic definitions and properties of the associated braid groups, as well as a quick introduction to Bessis' lifting of Springer theory to braid groups.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1988
606   $aGroup theory
606   $aCommutative algebra
606   $aCommutative rings
606   $aAssociative rings
606   $aRings (Algebra)
606   $aAlgebraic topology
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019
615  0$aGroup theory.
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAssociative rings.
615  0$aRings (Algebra).
615  0$aAlgebraic topology.
615 14$aGroup Theory and Generalizations.
615 24$aCommutative Rings and Algebras.
615 24$aAssociative Rings and Algebras.
615 24$aAlgebraic Topology.
676   $a512.2
686   $aMAT 203f$2stub
686   $aSI 850$2rvk
700   $aBroué$b Michel$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478936
906   $aBOOK
912   $a996466502903316
996   $aIntroduction to complex reflection groups and their braid groups$9261779
997   $aUNISA