File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: The strong Anick conjecture

TitleThe strong Anick conjecture
Authors
KeywordsAutomorphisms
Free associative algebras
Tame coordinates
Wild coordinates
Issue Date2006
PublisherNational Academy of Sciences. The Journal's web site is located at http://www.pnas.org
Citation
Proceedings Of The National Academy Of Sciences Of The United States Of America, 2006, v. 103 n. 13, p. 4836-4840 How to Cite?
AbstractRecently, Umirbaev 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 work, 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 discover a large, previously undescribed class of wild automorphisms of K(x, y, z) that is not covered by the results of Umirbaev. © 2006 by The National Academy of Sciences of the USA.
Persistent Identifierhttp://hdl.handle.net/10722/75210
ISSN
2015 Impact Factor: 9.423
2015 SCImago Journal Rankings: 6.883
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorDrensky, Ven_HK
dc.contributor.authorYu, JTen_HK
dc.date.accessioned2010-09-06T07:08:59Z-
dc.date.available2010-09-06T07:08:59Z-
dc.date.issued2006en_HK
dc.identifier.citationProceedings Of The National Academy Of Sciences Of The United States Of America, 2006, v. 103 n. 13, p. 4836-4840en_HK
dc.identifier.issn0027-8424en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75210-
dc.description.abstractRecently, Umirbaev 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 work, 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 discover a large, previously undescribed class of wild automorphisms of K(x, y, z) that is not covered by the results of Umirbaev. © 2006 by The National Academy of Sciences of the USA.en_HK
dc.languageengen_HK
dc.publisherNational Academy of Sciences. The Journal's web site is located at http://www.pnas.orgen_HK
dc.relation.ispartofProceedings of the National Academy of Sciences of the United States of Americaen_HK
dc.subjectAutomorphismsen_HK
dc.subjectFree associative algebrasen_HK
dc.subjectTame coordinatesen_HK
dc.subjectWild coordinatesen_HK
dc.titleThe strong Anick conjectureen_HK
dc.typeArticleen_HK
dc.identifier.emailYu, JT:yujt@hku.hken_HK
dc.identifier.authorityYu, JT=rp00834en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1073/pnas.0509951103en_HK
dc.identifier.scopuseid_2-s2.0-33645520655en_HK
dc.identifier.hkuros122790en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33645520655&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume103en_HK
dc.identifier.issue13en_HK
dc.identifier.spage4836en_HK
dc.identifier.epage4840en_HK
dc.identifier.isiWOS:000236472500011-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridDrensky, V=6603826254en_HK
dc.identifier.scopusauthoridYu, JT=7405530208en_HK

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats