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Article: Automorphisms fixing a variable of K 〈x, y, z〉

TitleAutomorphisms fixing a variable of K 〈x, y, z〉
Authors
KeywordsAutomorphisms Of Free And Polynomial Algebras
Tame Automorphisms
Wild Automorphisms
Issue Date2005
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 2005, v. 291 n. 1, p. 250-258 How to Cite?
AbstractWe study automorphisms of φ the free associative algebra K 〈x, y, z〉 over a field K such that φ(x), φ(y) are linear with respect to x, y and φ(z) = z. We establish a sufficient and necessary condition for the tameness of these automorphisms in the class of all automorphisms fixing z, which gives an algorithm to recognize the wild ones. In particular, we prove that the well-known Anick automorphism is wild in this sense. This class of automorphisms induces tame automorphisms of the polynomial algebra K[x, y, z]. For n > 2 the automorphisms of K 〈x1,..., xn, z〉 which fix z and are linear in the xis are tame. © 2005 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/156142
ISSN
2015 Impact Factor: 0.66
2015 SCImago Journal Rankings: 1.165
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorDrensky, Ven_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:34Z-
dc.date.available2012-08-08T08:40:34Z-
dc.date.issued2005en_US
dc.identifier.citationJournal Of Algebra, 2005, v. 291 n. 1, p. 250-258en_US
dc.identifier.issn0021-8693en_US
dc.identifier.urihttp://hdl.handle.net/10722/156142-
dc.description.abstractWe study automorphisms of φ the free associative algebra K 〈x, y, z〉 over a field K such that φ(x), φ(y) are linear with respect to x, y and φ(z) = z. We establish a sufficient and necessary condition for the tameness of these automorphisms in the class of all automorphisms fixing z, which gives an algorithm to recognize the wild ones. In particular, we prove that the well-known Anick automorphism is wild in this sense. This class of automorphisms induces tame automorphisms of the polynomial algebra K[x, y, z]. For n > 2 the automorphisms of K 〈x1,..., xn, z〉 which fix z and are linear in the xis are tame. © 2005 Elsevier Inc. All rights reserved.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_US
dc.relation.ispartofJournal of Algebraen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectAutomorphisms Of Free And Polynomial Algebrasen_US
dc.subjectTame Automorphismsen_US
dc.subjectWild Automorphismsen_US
dc.titleAutomorphisms fixing a variable of K 〈x, y, z〉en_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturepostprinten_US
dc.identifier.doi10.1016/j.jalgebra.2005.04.009en_US
dc.identifier.scopuseid_2-s2.0-23844539945en_US
dc.identifier.hkuros115351-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-23844539945&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume291en_US
dc.identifier.issue1en_US
dc.identifier.spage250en_US
dc.identifier.epage258en_US
dc.identifier.isiWOS:000231515500014-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridDrensky, V=6603826254en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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