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Article: Dimension of automorphisms with fixed degree for free algebras of Nielsen-Schreier varieties

TitleDimension of automorphisms with fixed degree for free algebras of Nielsen-Schreier varieties
Authors
KeywordsAutomorphisms
Coordinates
Dimension
Nielsen-Schreier Varieties
Issue Date2009
Citation
Comptes Rendus De L'academie Bulgare Des Sciences, 2009, v. 62 n. 1, p. 9-16 How to Cite?
AbstractLet ℳ be a Nielsen-Schreier variety of algebras over an algebraically closed field and let F(x, y) be an ℳ-free algebra on two generators. Assume that the sequence of dimensions c n of the homogeneous polynomials of degree n in F(x) satisfies the inequalities 1 = c 1 = c 2 ≤ c 3 ≤ ···. We establish that the set of automorphisms (f, g) of F(x, y) such that n = max{deg(f), deg(g)} forms a constructible set with dimension d n = c 1 + c 2+ ··· + c n + 4 + 2E, where E = 1 for unital algebras and E = 0 for nonunital algebras. The dimension of the set of coordinates f of degree n is equal to c 1 + c 2 + ··· + c n + 2 + E.
Persistent Identifierhttp://hdl.handle.net/10722/156240
ISSN
2015 Impact Factor: 0.233
References

 

DC FieldValueLanguage
dc.contributor.authorDrensky, Ven_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:59Z-
dc.date.available2012-08-08T08:40:59Z-
dc.date.issued2009en_US
dc.identifier.citationComptes Rendus De L'academie Bulgare Des Sciences, 2009, v. 62 n. 1, p. 9-16en_US
dc.identifier.issn1310-1331en_US
dc.identifier.urihttp://hdl.handle.net/10722/156240-
dc.description.abstractLet ℳ be a Nielsen-Schreier variety of algebras over an algebraically closed field and let F(x, y) be an ℳ-free algebra on two generators. Assume that the sequence of dimensions c n of the homogeneous polynomials of degree n in F(x) satisfies the inequalities 1 = c 1 = c 2 ≤ c 3 ≤ ···. We establish that the set of automorphisms (f, g) of F(x, y) such that n = max{deg(f), deg(g)} forms a constructible set with dimension d n = c 1 + c 2+ ··· + c n + 4 + 2E, where E = 1 for unital algebras and E = 0 for nonunital algebras. The dimension of the set of coordinates f of degree n is equal to c 1 + c 2 + ··· + c n + 2 + E.en_US
dc.languageengen_US
dc.relation.ispartofComptes Rendus de L'Academie Bulgare des Sciencesen_US
dc.subjectAutomorphismsen_US
dc.subjectCoordinatesen_US
dc.subjectDimensionen_US
dc.subjectNielsen-Schreier Varietiesen_US
dc.titleDimension of automorphisms with fixed degree for free algebras of Nielsen-Schreier varietiesen_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturepostprint-
dc.identifier.scopuseid_2-s2.0-64049109129en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-64049109129&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume62en_US
dc.identifier.issue1en_US
dc.identifier.spage9en_US
dc.identifier.epage16en_US
dc.publisher.placeBulgariaen_US
dc.identifier.scopusauthoridDrensky, V=6603826254en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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