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Article: The strong anick conjecture is true

TitleThe strong anick conjecture is true
Authors
KeywordsAutomorphisms Of Free And Polynomial Algebras
Coordinates In Free Algebras
Tame Automorphisms
Wild Automorphisms
Issue Date2007
Citation
Journal Of The European Mathematical Society, 2007, v. 9 n. 4, p. 659-679 How to Cite?
AbstractRecently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K〉x, y, z〈 over a field K of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of K〈x, y, z〉. In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a similar result for several large classes of automorphisms of K〈x, y, z〉. We also find a large new class of wild automorphisms of K〈x, y, z〉 which is not covered by the results of Umirbaev. Finally, we study the lifting problem for automorphisms and coordinates of polynomial algebras, free metabelian algebras and free associative algebras and obtain some interesting new results. © European Mathematical Society 2007.
Persistent Identifierhttp://hdl.handle.net/10722/156199
ISSN
2015 Impact Factor: 1.95
2015 SCImago Journal Rankings: 3.658
References

 

DC FieldValueLanguage
dc.contributor.authorDrensky, Ven_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:49Z-
dc.date.available2012-08-08T08:40:49Z-
dc.date.issued2007en_US
dc.identifier.citationJournal Of The European Mathematical Society, 2007, v. 9 n. 4, p. 659-679en_US
dc.identifier.issn1435-9855en_US
dc.identifier.urihttp://hdl.handle.net/10722/156199-
dc.description.abstractRecently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K〉x, y, z〈 over a field K of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of K〈x, y, z〉. In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a similar result for several large classes of automorphisms of K〈x, y, z〉. We also find a large new class of wild automorphisms of K〈x, y, z〉 which is not covered by the results of Umirbaev. Finally, we study the lifting problem for automorphisms and coordinates of polynomial algebras, free metabelian algebras and free associative algebras and obtain some interesting new results. © European Mathematical Society 2007.en_US
dc.languageengen_US
dc.relation.ispartofJournal of the European Mathematical Societyen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectAutomorphisms Of Free And Polynomial Algebrasen_US
dc.subjectCoordinates In Free Algebrasen_US
dc.subjectTame Automorphismsen_US
dc.subjectWild Automorphismsen_US
dc.titleThe strong anick conjecture is trueen_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturepostprinten_US
dc.identifier.scopuseid_2-s2.0-36348942874en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-36348942874&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume9en_US
dc.identifier.issue4en_US
dc.identifier.spage659en_US
dc.identifier.epage679en_US
dc.identifier.scopusauthoridDrensky, V=6603826254en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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