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Peer-reviewedCC BY 4.0Mathematics

Central Test Set and Central Test Rank of Free Nilpotent Lie Algebras of Rank 2

  • Özge Öztekin1
  1. 1Department of Mathematics, Faculty of Arts and Sciences, Gaziantep University, 27310 Gaziantep, Türkiye
Open at sourceDOICite

Abstract

In this paper, we introduce and establish the concept of a central test set for free nilpotent Lie algebras. We prove that the central test rank of a free nilpotent Lie algebra Lc,2 of rank 2 and nilpotency class c = 3 equals 3. Furthermore, we show that a minimal central test set of L3,2 belongs to the lower-degree bracket structures and is explicitly given by the set 𝒯 = {[x,y], [[x,y],x], [x,y],y}. We also analyze higher nilpotency classes c ≥ 4 and delineate the degree conditions under which elements effectively eliminate non-central derivations.

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Cite

BibTeXRIS
BibTeX
@article{oztekin2026central,
  title = {{Central Test Set and Central Test Rank of Free Nilpotent Lie Algebras of Rank 2}},
  author = {Özge Öztekin},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203771},
  url = {https://www.mdpi.com/2227-7390/14/20/3771},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Central Test Set and Central Test Rank of Free Nilpotent Lie Algebras of Rank 2
AU  - Özge Öztekin
PY  - 2026
DA  - 2026/10/17
JO  - Mathematics
DO  - 10.3390/math14203771
UR  - https://www.mdpi.com/2227-7390/14/20/3771
AB  - In this paper, we introduce and establish the concept of a central test set for free nilpotent Lie algebras. We prove that the central test rank of a free nilpotent Lie algebra Lc,2 of rank 2 and nilpotency class c = 3 equals 3. Furthermore, we show that a minimal central test set of L3,2 belongs to the lower-degree bracket structures and is explicitly given by the set 𝒯 = {[x,y], [[x,y],x], [x,y],y}. We also analyze higher nilpotency classes c ≥ 4 and delineate the degree conditions under which elements effectively eliminate non-central derivations.
SN  - 2227-7390
ER  -