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Article: Automorphic orbits in free non-associative algebras

TitleAutomorphic orbits in free non-associative algebras
Authors
Mikhalev, AAUmirbaev, UYu, JT
Issue Date2001
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra
Citation
Journal Of Algebra, 2001, v. 243 n. 1, p. 198-223 How to Cite?
DOI: http://dx.doi.org/10.1006/jabr.2001.8794
AbstractWe consider finitely generated free non-associative algebras, free commutative non-associative algebras, and free anti-commutative non-associative algebras. We study orbits of elements of these algebras under the action of automorphism groups. Using free differential calculus we obtain matrix criteria for a system of elements to have given rank (or to be primitive). It gives us a possibility to construct fast algorithm to recognize primitive systems of elements. We show that if an endomorphism of a free algebra preserves the automorphic orbit of a nonzero element, then it is an automorphism of this algebra. In particular, endomorphisms preserving primitivity of elements are automorphisms. © 2001 Academic Press.
Persistent Identifierhttp://hdl.handle.net/10722/75414
ISSN
0021-8693
2023 Impact Factor: 0.8
2023 SCImago Journal Rankings: 1.023
ISI Accession Number ID
WOS:000170882200011
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorMikhalev, AAen_HK
dc.contributor.authorUmirbaev, Uen_HK
dc.contributor.authorYu, JTen_HK
dc.date.accessioned2010-09-06T07:10:53Z-
dc.date.available2010-09-06T07:10:53Z-
dc.date.issued2001en_HK
dc.identifier.citationJournal Of Algebra, 2001, v. 243 n. 1, p. 198-223en_HK
dc.identifier.issn0021-8693en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75414-
dc.description.abstractWe consider finitely generated free non-associative algebras, free commutative non-associative algebras, and free anti-commutative non-associative algebras. We study orbits of elements of these algebras under the action of automorphism groups. Using free differential calculus we obtain matrix criteria for a system of elements to have given rank (or to be primitive). It gives us a possibility to construct fast algorithm to recognize primitive systems of elements. We show that if an endomorphism of a free algebra preserves the automorphic orbit of a nonzero element, then it is an automorphism of this algebra. In particular, endomorphisms preserving primitivity of elements are automorphisms. © 2001 Academic Press.en_HK
dc.languageengen_HK
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_HK
dc.relation.ispartofJournal of Algebraen_HK
dc.titleAutomorphic orbits in free non-associative algebrasen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0021-8693&volume=243&issue=1&spage=198&epage=223&date=2001&atitle=Automorphic+orbits+in+free+non-associative+algebrasen_HK
dc.identifier.emailYu, JT:yujt@hku.hken_HK
dc.identifier.authorityYu, JT=rp00834en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1006/jabr.2001.8794en_HK
dc.identifier.scopuseid_2-s2.0-0035455608en_HK
dc.identifier.hkuros66848en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0035455608&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume243en_HK
dc.identifier.issue1en_HK
dc.identifier.spage198en_HK
dc.identifier.epage223en_HK
dc.identifier.isiWOS:000170882200011-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridMikhalev, AA=7007020926en_HK
dc.identifier.scopusauthoridUmirbaev, U=6603525344en_HK
dc.identifier.scopusauthoridYu, JT=7405530208en_HK
dc.identifier.issnl0021-8693-

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