Bases of fixed point subalgebras on nilpotent Leibniz algebras

Year 2024, Volume: 26 Issue: 1, 272 - 278, 19.01.2024

Zeynep Yaptı Özkurt

https://doi.org/10.25092/baunfbed.1332488

Abstract

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.

Keywords

nilpotent Leibniz algebra, fixed point, automorphism

Nilpotent Leibniz cebirlerinde sabit nokta altcebirlerinin bazları

Abstract

K karakteristiği 0 olan bir cisim, X={x_(1,) x_2,…,x_n} ve R_m={r_(1,) ,…,r_m} iki değişkenler kümesi, F, K cismi üzerinde X tarafından üretilen bir serbest sol nilpotent Leibniz cebiri ve K[R_m ], K cismi üzerinde R_m tarafından üretilen komutatif polinomlar cebiri olsunlar. F nin bir φ otomorfizminin sabit nokta altcebiri, F nin bu otomorfizm altında invaryant kalan elemanlarını içeren altcebiridir. Bu çalışmada F nin bazı özel otomorfizmleri ele alınarak bu otomorfizmlerin sabit nokta altcebirleri belirlenmiştir. Sonra, bu sabit nokta altcebirlerinin baz kümeleri elde edilmiştir. Daha sonra bu altcebirlerin serbest K[R_m ]-modülü olarak üreteçleri verilmiştir.

Keywords

nilpotent Leibniz cebirleri, sabit nokta, otomorfizm

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