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This article is cited in 2 scientific papers (total in 2 papers)
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 stк., Kostanay, 110000, Kazakhstan
b L.N. Gumilyov Eurasian National University, 2, Satpaev str., Nur-Sultan, 010008, Kazakhstan
Abstract:
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, automorphism, free product, linearization, triangulation.
Received December 19, 2018, published August 20, 2019
Citation:
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
Linking options:
https://www.mathnet.ru/eng/semr1118 https://www.mathnet.ru/eng/semr/v16/p1133
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