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Article: On the lifting of the Nagata automorphism

TitleOn the lifting of the Nagata automorphism
Authors
KeywordsAutomorphisms
Canonical Decomposation
Coordinates
Degree Estimate
Free Associative Algebras
Lifting
Nagata
Polynomial Algebras
Sandwich
Stable Tameness
Tame
Wild
Issue Date2011
PublisherBirkhaeuser Verlag AG. The Journal's web site is located at http://link.springer.de/link/service/journals/00029/index.htm
Citation
Selecta Mathematica, New Series, 2011, v. 17 n. 4, p. 935-945 How to Cite?
AbstractIt is proved that all wild z-automorphisms including the well-known Nagata automorphism (all wild z-coordinates including the Nagata coordinates, respectively) of the polynomial algebra F[x, y, z] over an arbitrary field F cannot be lifted to a z-automorphism (z-coordinate, respectively) of the free associative algebra 〈x, y, z〉. The proof is based on the following two new results, which have their own interests: degree estimate of Q *F F〈x 1, ..., x n〉 and tameness of the automorphism group Aut q(Q * F F〈x, y〉). The structure of the group of all z-automorphisms of the free associative algebra F〈x, y〉 over an arbitrary field F is also determined. © 2011 Springer Basel AG.
Persistent Identifierhttp://hdl.handle.net/10722/156276
ISSN
2015 Impact Factor: 1.148
2015 SCImago Journal Rankings: 2.138
ISI Accession Number ID
Funding AgencyGrant Number
RGC-GRF
Funding Information:

The research of Jie-Tai Yu was partially supported by an RGC-GRF Grant.

References

 

DC FieldValueLanguage
dc.contributor.authorBelovKanel, Aen_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:41:08Z-
dc.date.available2012-08-08T08:41:08Z-
dc.date.issued2011en_US
dc.identifier.citationSelecta Mathematica, New Series, 2011, v. 17 n. 4, p. 935-945en_US
dc.identifier.issn1022-1824en_US
dc.identifier.urihttp://hdl.handle.net/10722/156276-
dc.description.abstractIt is proved that all wild z-automorphisms including the well-known Nagata automorphism (all wild z-coordinates including the Nagata coordinates, respectively) of the polynomial algebra F[x, y, z] over an arbitrary field F cannot be lifted to a z-automorphism (z-coordinate, respectively) of the free associative algebra 〈x, y, z〉. The proof is based on the following two new results, which have their own interests: degree estimate of Q *F F〈x 1, ..., x n〉 and tameness of the automorphism group Aut q(Q * F F〈x, y〉). The structure of the group of all z-automorphisms of the free associative algebra F〈x, y〉 over an arbitrary field F is also determined. © 2011 Springer Basel AG.en_US
dc.languageengen_US
dc.publisherBirkhaeuser Verlag AG. The Journal's web site is located at http://link.springer.de/link/service/journals/00029/index.htmen_US
dc.relation.ispartofSelecta Mathematica, New Seriesen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectAutomorphismsen_US
dc.subjectCanonical Decomposationen_US
dc.subjectCoordinatesen_US
dc.subjectDegree Estimateen_US
dc.subjectFree Associative Algebrasen_US
dc.subjectLiftingen_US
dc.subjectNagataen_US
dc.subjectPolynomial Algebrasen_US
dc.subjectSandwichen_US
dc.subjectStable Tamenessen_US
dc.subjectTameen_US
dc.subjectWilden_US
dc.titleOn the lifting of the Nagata automorphismen_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturepostprinten_US
dc.identifier.doi10.1007/s00029-011-0061-3en_US
dc.identifier.scopuseid_2-s2.0-81955160878en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-81955160878&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume17en_US
dc.identifier.issue4en_US
dc.identifier.spage935en_US
dc.identifier.epage945en_US
dc.identifier.eissn1420-9020-
dc.identifier.isiWOS:000297498800006-
dc.publisher.placeSwitzerlanden_US
dc.identifier.scopusauthoridBelovKanel, A=22033716200en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US
dc.identifier.citeulike9272238-

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