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Article: Automorphic equivalence problem for free associative algebras of rank two
Title | Automorphic equivalence problem for free associative algebras of rank two |
---|---|
Authors | |
Keywords | Automorphic Equivalence In Free Algebras Automorphisms Of Free And Polynomial Algebras |
Issue Date | 2007 |
Publisher | World 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? |
Abstract | Let 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 In our approach we combine an idea of the latter three authors with an idea from the unpublished thesis of Lane used to describe automorphisms which stabilize elements of K 〈x, y〉.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 Identifier | http://hdl.handle.net/10722/156184 |
ISSN | 2015 Impact Factor: 0.469 2015 SCImago Journal Rankings: 0.771 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Drensky, V | en_US |
dc.contributor.author | Yu, JT | en_US |
dc.date.accessioned | 2012-08-08T08:40:45Z | - |
dc.date.available | 2012-08-08T08:40:45Z | - |
dc.date.issued | 2007 | en_US |
dc.identifier.citation | International Journal Of Algebra And Computation, 2007, v. 17 n. 2, p. 221-234 | en_US |
dc.identifier.issn | 0218-1967 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156184 | - |
dc.description.abstract | Let 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.language | eng | en_US |
dc.publisher | World Scientific Publishing Co Pte Ltd. The Journal's web site is located at http://www.worldscinet.com/ijac/ijac.shtml | en_US |
dc.relation.ispartof | International Journal of Algebra and Computation | en_US |
dc.rights | Creative Commons: Attribution 3.0 Hong Kong License | - |
dc.subject | Automorphic Equivalence In Free Algebras | en_US |
dc.subject | Automorphisms Of Free And Polynomial Algebras | en_US |
dc.title | Automorphic equivalence problem for free associative algebras of rank two | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yu, JT:yujt@hku.hk | en_US |
dc.identifier.authority | Yu, JT=rp00834 | en_US |
dc.description.nature | postprint | en_US |
dc.identifier.doi | 10.1142/S0218196707003573 | en_US |
dc.identifier.scopus | eid_2-s2.0-33947633430 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-33947633430&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 17 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.spage | 221 | en_US |
dc.identifier.epage | 234 | en_US |
dc.identifier.isi | WOS:000250893900001 | - |
dc.publisher.place | Singapore | en_US |
dc.identifier.scopusauthorid | Drensky, V=6603826254 | en_US |
dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_US |