TY  - JOUR
TI  - On the Orbit Problem of Free Lie Algebras
AB  - By operationalizing Fn as a free Lie Algebra of finite rank n, this work considers the orbit problem for Fn. The orbit problem is the following: given an element u ∈ Fn and a finitely generated subalgebra H of Fn, does H meet the orbit of u under the automorphism group AutFn of Fn? It is proven that the orbit problem is decidable for finite rank n, n ⩾ 2. Furthermore, we solve a particular instance of the problem – i.e., whether H contains a primitive element of Fn. In addition, some applications are provided. Finally, the paper inquires the need for further research.
AU  - OZKURT, ZEYNEP
DO  - 10.53570/jnt.1284897
PY  - 2023
JO  - Journal of New Theory
IS  - 43
SN  - 2149-1402
SP  - 83
EP  - 91
DB  - TRDizin
UR  - http://search/yayin/detay/1187131
ER  -