Geodesic
Linearization of automorphisms and triangulation of derivations of free algebras of rank 2
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1133-1146

Voir la notice de l'article provenant de la source Math-Net.Ru

We define a class of $\circ$-varieties of algebras and prove that the tame automorphism group of a free algebra of rank two of any $\circ$-variety of algebras over a field admits an amalgamated free product structure. In particular, the automorphism group of a free right-symmetric algebra of rank two admits an amalgamated free product structure. Using this structure, we prove that any locally finite group of automorphisms of this algebra is conjugate to a subgroup of affine or triangular automorphisms. This implies that any reductive group of automorphisms of a two-generated free right-symmetric algebra is linearizable and any locally nilpotent derivation of this algebra is triangulable over a field of characteristic zero. All of these results are true for free commutative and free non-associative algebras of rank two.
Keywords: free right-symmetric algebra, free product, linearization
Mots-clés : automorphism, triangulation. 
@article{SEMR_2019_16_a18,
     author = {A. A. Alimbaev and A. S. Naurazbekova and D. Kh. Kozybaev},
     title = {Linearization of automorphisms and triangulation of derivations of free algebras of rank 2},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1133--1146},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a18/}
}
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A. A. Alimbaev; A. S. Naurazbekova; D. Kh. Kozybaev. Linearization of automorphisms and triangulation of derivations of free algebras of rank 2. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1133-1146. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a18/