Automorphisms of free metabelian Leibniz algebras

Adiyaman, Tuba Taş; Özkurt, Zeynep

doi:10.1080/00927872.2021.1919690

Cited by 6 publications

(2 citation statements)

References 8 publications

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“…Additionally, Abanina and Mishchenko investigated the variety of left nilpotent Leibniz algebras of class 3 defined by the polynomial identity [𝑥1,[𝑥2,[𝑥3,𝑥4]]]=0 [6]. On the relatively free Leibniz algebras, for more details see the works [7][8][9][10][11]. In [12], Drensky and Papistas obtained a generating set of the automorphism group of free nilpotent Leibniz algebras and they show that the fixed points subalgebra is not finitely generated.…”

Section: Introductionmentioning

confidence: 99%

Bases of fixed point subalgebras on nilpotent Leibniz algebras

YAPTI ÖZKURT

2024

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Let K be a field of characteristic zero, X={x_(1,) x_2,…,x_n} and R_m={r_(1,) ,…,r_m} be two sets of variables, F be the free left nitpotent Leibniz algebra generated by X, and K[R_m ] be the commutative polynomial algebra generated by R_m over the base field K. The fixed point subalgebra of an automorphism φ is the subalgebra of F consisting of elements that are invariant under the automorphism. In this work, we consider specific automorphisms of F and determine the fixed point subalgebras of these automorphisms. Then, we find bases of these fixed point subalgebras. In addition, we get generators of these subalgebras as a free K[R_m ] -module.

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Section: Introductionmentioning

confidence: 99%

Bases of fixed point subalgebras on nilpotent Leibniz algebras

YAPTI ÖZKURT

2024

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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“…The kernel of π is called the IA-automorphism group and denoted by IAut(M). In [17,18], the author and Taş Adıyaman described a generating set for IAut(M) of rank three and n, respectively. Recently, symmetric 148 Z. ÖZKURT polynomials of M were considered in [7].…”

Section: Introductionmentioning

confidence: 99%

Normal automorphisms of free metabelian Leibniz algebras

YAPTI ÖZKURT

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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Let $\mathfrak{M}$ be a free metabelian Leibniz algebra generating set $% X=\{x_{1},...,x_{n}\}$ over the field $K$ of characteristic $0$. An automorphism $ \phi $ of $\mathfrak{M}$ is said to be normal automorphism if each ideal of $\mathfrak{M}$ is invariant under $ \phi $. In this work, it is proven that every normal automorphism of $\mathfrak{M}$ is an IA-automorphism and the group of normal automorphisms coincides with the group of inner automorphisms.

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Endomorphisms which preserve orbits of free metabelian Leibniz algebras

Adiyaman Taş,

Özkurt

2023

Communications in Algebra

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Automorphisms of free metabelian Leibniz algebras

Cited by 6 publications

References 8 publications

Bases of fixed point subalgebras on nilpotent Leibniz algebras

Bases of fixed point subalgebras on nilpotent Leibniz algebras

Normal automorphisms of free metabelian Leibniz algebras

Endomorphisms which preserve orbits of free metabelian Leibniz algebras

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