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Article: Automorphic equivalence problem for free associative algebras of rank two

TitleAutomorphic equivalence problem for free associative algebras of rank two
Authors
KeywordsAutomorphic Equivalence In Free Algebras
Automorphisms Of Free And Polynomial Algebras
Issue Date2007
PublisherWorld Scientific Publishing Co Pte Ltd. The Journal's web site is located at http://www.worldscinet.com/ijac/ijac.shtml
Citation
International Journal Of Algebra And Computation, 2007, v. 17 n. 2, p. 221-234 How to Cite?
AbstractLet K 〈x, y〉 be the free associative algebra of rank 2 over an algebraically closed constructive field of any characteristic. We present an algorithm which decides whether or not two elements in K 〈x, y〉 are equivalent under an automorphism of K 〈x, y〉. A modification of our algorithm solves the problem whether or not an element in K 〈x, y〉 is a semiinvariant of a nontrivial automorphism. In particular, it determines whether or not the element has a nontrivial stabilizer in Aut K 〈x, y〉. An algorithm for equivalence of polynomials under automorphisms of ℂ[x, y] was presented by Wightwick. Another, much simpler algorithm for automorphic equivalence of two polynomials in K[x, y] for any algebraically closed constructive field K was given by Makar-Limanov, Shpilrain, and Yu. In our approach we combine an idea of the latter three authors with an idea from the unpublished thesis of Lane used to describe automorphisms which stabilize elements of K 〈x, y〉. This also allows us to give a simple proof of the corresponding result for K[x, y] obtained by Makar-Limanov, Shpilrain, and Yu. © World Scientific Publishing Company.
Persistent Identifierhttp://hdl.handle.net/10722/156184
ISSN
2015 Impact Factor: 0.469
2015 SCImago Journal Rankings: 0.771
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorDrensky, Ven_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:45Z-
dc.date.available2012-08-08T08:40:45Z-
dc.date.issued2007en_US
dc.identifier.citationInternational Journal Of Algebra And Computation, 2007, v. 17 n. 2, p. 221-234en_US
dc.identifier.issn0218-1967en_US
dc.identifier.urihttp://hdl.handle.net/10722/156184-
dc.description.abstractLet K 〈x, y〉 be the free associative algebra of rank 2 over an algebraically closed constructive field of any characteristic. We present an algorithm which decides whether or not two elements in K 〈x, y〉 are equivalent under an automorphism of K 〈x, y〉. A modification of our algorithm solves the problem whether or not an element in K 〈x, y〉 is a semiinvariant of a nontrivial automorphism. In particular, it determines whether or not the element has a nontrivial stabilizer in Aut K 〈x, y〉. An algorithm for equivalence of polynomials under automorphisms of ℂ[x, y] was presented by Wightwick. Another, much simpler algorithm for automorphic equivalence of two polynomials in K[x, y] for any algebraically closed constructive field K was given by Makar-Limanov, Shpilrain, and Yu. In our approach we combine an idea of the latter three authors with an idea from the unpublished thesis of Lane used to describe automorphisms which stabilize elements of K 〈x, y〉. This also allows us to give a simple proof of the corresponding result for K[x, y] obtained by Makar-Limanov, Shpilrain, and Yu. © World Scientific Publishing Company.en_US
dc.languageengen_US
dc.publisherWorld Scientific Publishing Co Pte Ltd. The Journal's web site is located at http://www.worldscinet.com/ijac/ijac.shtmlen_US
dc.relation.ispartofInternational Journal of Algebra and Computationen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectAutomorphic Equivalence In Free Algebrasen_US
dc.subjectAutomorphisms Of Free And Polynomial Algebrasen_US
dc.titleAutomorphic equivalence problem for free associative algebras of rank twoen_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturepostprinten_US
dc.identifier.doi10.1142/S0218196707003573en_US
dc.identifier.scopuseid_2-s2.0-33947633430en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33947633430&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume17en_US
dc.identifier.issue2en_US
dc.identifier.spage221en_US
dc.identifier.epage234en_US
dc.identifier.isiWOS:000250893900001-
dc.publisher.placeSingaporeen_US
dc.identifier.scopusauthoridDrensky, V=6603826254en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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