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Article: Fixed points of endomorphisms of a free metabelian group

TitleFixed points of endomorphisms of a free metabelian group
Authors
KeywordsMathematics physics
Issue Date1998
PublisherCambridge University Press.
Citation
Mathematical Proceedings of the Cambridge Philosophical Society, 1998, v. 123 n. 1, p. 75-83 How to Cite?
AbstractWe consider IA-endomorphisms (i.e. Identical in Abelianization) of a free metabelian group of finite rank, and give a matrix characterization of their fixed points which is similar to (yet different from) the well-known characterization of eigenvectors of a linear operator in a vector space. We then use our matrix characterization to elaborate several properties of the fixed point groups of metabelian endomorphisms. In particular, we show that the rank of the fixed point group of an IA-endomorphism of the free metabelian group of rank n[gt-or-equal, slanted]2 can be either equal to 0, 1, or greater than (n−1) (in particular, it can be infinite). We also point out a connection between these properties of metabelian IA-endomorphisms and some properties of the Gassner representation of pure braid groups.
Persistent Identifierhttp://hdl.handle.net/10722/53387
ISSN
2015 Impact Factor: 0.534
2015 SCImago Journal Rankings: 1.069

 

DC FieldValueLanguage
dc.contributor.authorShpilrain, Ven_HK
dc.date.accessioned2009-04-03T07:18:25Z-
dc.date.available2009-04-03T07:18:25Z-
dc.date.issued1998en_HK
dc.identifier.citationMathematical Proceedings of the Cambridge Philosophical Society, 1998, v. 123 n. 1, p. 75-83en_HK
dc.identifier.issn0305-0041en_HK
dc.identifier.urihttp://hdl.handle.net/10722/53387-
dc.description.abstractWe consider IA-endomorphisms (i.e. Identical in Abelianization) of a free metabelian group of finite rank, and give a matrix characterization of their fixed points which is similar to (yet different from) the well-known characterization of eigenvectors of a linear operator in a vector space. We then use our matrix characterization to elaborate several properties of the fixed point groups of metabelian endomorphisms. In particular, we show that the rank of the fixed point group of an IA-endomorphism of the free metabelian group of rank n[gt-or-equal, slanted]2 can be either equal to 0, 1, or greater than (n−1) (in particular, it can be infinite). We also point out a connection between these properties of metabelian IA-endomorphisms and some properties of the Gassner representation of pure braid groups.en_HK
dc.languageengen_HK
dc.publisherCambridge University Press.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsMathematical Proceedings of the Cambridge Philosophical Society. Copyright © Cambridge University Press.en_HK
dc.subjectMathematics physicsen_HK
dc.titleFixed points of endomorphisms of a free metabelian groupen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0305-0041&volume=123&issue=1&spage=75&epage=83&date=1998&atitle=Fixed+points+of+endomorphisms+of+a+free+metabelian+groupen_HK
dc.identifier.emailShpilrain, V: shpil@submaths.hku.hken_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.hkuros36438-

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