Automorphisms and derivations of a universal left-symmetric enveloping algebra
Zhangazinova D. Naurazbekova A. Umirbaev U.
15 March 2026Academic Press Inc.
Journal of Algebra
2026#690701 - 729 pp.
Let An be an n-dimensional algebra with zero multiplication over a field K of characteristic 0. Then its universal (multiplicative) enveloping algebra Un in the variety of left-symmetric algebras is a homogeneous quadratic algebra generated by 2n elements l1,…,ln,r1,…,rn, which contains both the polynomial algebra Ln=K[l1,…,ln] and the free associative algebra Rn=K〈r1,…,rn〉. We show that the automorphism groups of the polynomial algebra Ln and the algebra Un are isomorphic for all n≥2, based on a detailed analysis of locally nilpotent derivations. In contrast, we show that this isomorphism does not hold for n=1, and we provide a complete description of all automorphisms and locally nilpotent derivations of U1.
Associative algebra , Automorphism , Derivation , Left-symmetric algebra , Polynomial algebra , Universal enveloping algebra
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L.N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan
Department of Mathematics, Wayne State University, Detroit, 48202, MI, United States
Department of Mathematics, Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
L.N. Gumilyov Eurasian National University
Department of Mathematics
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026