The local structure of groups of triangular automorphisms of relatively free algebras.

DOI10.1007/s10469-012-9202-9zbMath1270.16031OpenAlexW1976601730MaRDI QIDQ1936276

Vitaliĭ Roman'kov

Publication date: 21 February 2013

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-012-9202-9

zbMATH Keywords

polynomial algebrasfree associative algebrasmatrix representationsresidual finitenessrelatively free algebrasgroups of triangular automorphismsabsolutely free algebrasgroups of unitriangular automorphismswidth of commutator subgroup

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Ordinary and skew polynomial rings and semigroup rings (16S36) Generators, relations, and presentations of groups (20F05) Automorphisms and endomorphisms (16W20) Jacobian problem (14R15) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) (14R10) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Commutator calculus (20F12) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36) Free nonassociative algebras (17A50)

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Cites Work

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• The tame and the wild automorphisms of polynomial rings in three variables
• Automorphisms of a Free Associative Algebra of Rank 2.I
• Automorphisms of a Free Associative Algebra of Rank 2. II
• Über ganze birationale Transformationen der Ebene.

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