CHEIN AUTOMORPHISMS OF FREE METABELIAN ANTICOMMUTATIVE ALGEBRAS
Nauryzbaev R. Shestakov I. Umirbaev U.
23 December 2025Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
Serdica Mathematical Journal
2025#51Issue 3-4351 - 366 pp.
We describe all automorphisms of a free metabelian anticommutative algebra of rank n ≥ 3 over a field K that move only one variable while fixing the others. Such automorphisms are called Chein automorphisms in the cases of free metabelian groups and free metabelian Lie algebras. We show that all automorphisms of a free metabelian anticommutative algebra of rank n=2 are linear, and that the simplest non elementary Chein automorphism of degree 3 is absolutely wild for all n ≥ 3.
anticommutative algebra , automorphism , derivation , divergence , metabelian algebra
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Department of Mathematics, L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
Shenzhen International Center for Mathematics, Shenzhen, China
Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil
Department of Mathematics, Wayne State University, Detroit, United States
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics
Shenzhen International Center for Mathematics
Instituto de Matemática e Estatística
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
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