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Article: Automorphic orbits in free non-associative algebras
Title | Automorphic orbits in free non-associative algebras |
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Authors | |
Issue Date | 2001 |
Publisher | Academic 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? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/75414 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 1.023 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Mikhalev, AA | en_HK |
dc.contributor.author | Umirbaev, U | en_HK |
dc.contributor.author | Yu, JT | en_HK |
dc.date.accessioned | 2010-09-06T07:10:53Z | - |
dc.date.available | 2010-09-06T07:10:53Z | - |
dc.date.issued | 2001 | en_HK |
dc.identifier.citation | Journal Of Algebra, 2001, v. 243 n. 1, p. 198-223 | en_HK |
dc.identifier.issn | 0021-8693 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/75414 | - |
dc.description.abstract | We 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.language | eng | en_HK |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra | en_HK |
dc.relation.ispartof | Journal of Algebra | en_HK |
dc.title | Automorphic orbits in free non-associative algebras | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+algebras | en_HK |
dc.identifier.email | Yu, JT:yujt@hku.hk | en_HK |
dc.identifier.authority | Yu, JT=rp00834 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1006/jabr.2001.8794 | en_HK |
dc.identifier.scopus | eid_2-s2.0-0035455608 | en_HK |
dc.identifier.hkuros | 66848 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0035455608&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 243 | en_HK |
dc.identifier.issue | 1 | en_HK |
dc.identifier.spage | 198 | en_HK |
dc.identifier.epage | 223 | en_HK |
dc.identifier.isi | WOS:000170882200011 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Mikhalev, AA=7007020926 | en_HK |
dc.identifier.scopusauthorid | Umirbaev, U=6603525344 | en_HK |
dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_HK |
dc.identifier.issnl | 0021-8693 | - |