Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 1133–1146
Mathematical logic, algebra and number theory
Linearization of automorphisms and triangulation of derivations of free algebras of rank 2
A. A. Alimbaeva, A. S. Naurazbekovab, D. Kh. Kozybaevb
a U. Sultangazin Kostanay State Pedagogical University, 118, Tauelsizdik stê., Kostanay, 110000, Kazakhstan
b L.N. Gumilyov Eurasian National University, 2, Satpaev str., Nur-Sultan, 010008, Kazakhstan
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.
free right-symmetric algebra, automorphism, free product, linearization, triangulation.
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Received December 19, 2018, published August 20, 2019
A. A. Alimbaev, A. S. Naurazbekova, D. Kh. Kozybaev, “Linearization of automorphisms and triangulation of derivations of free algebras of rank 2”, Sib. Èlektron. Mat. Izv., 16 (2019), 1133–1146
Citation in format AMSBIB
\by A.~A.~Alimbaev, A.~S.~Naurazbekova, D.~Kh.~Kozybaev
\paper Linearization of automorphisms and triangulation of derivations of free algebras of rank 2
\jour Sib. \`Elektron. Mat. Izv.
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