The Structure of Primitive Leibniz Algebras via Maximal Subalgebras
Year: 2026
Type: article
Abstract: In this paper, we investigate the structure of primitive Leibniz algebras via their maximal subalgebras and minimal ideals. Using a two-sided definition of the centraliser, we show that the centraliser of a minimal ideal is again an ideal. Unlike the Lie algebra case, the use of this two-sided centraliser is essential in the Leibniz setting and accommodates genuinely new structural phenomena. In particular, we prove that a primitive Leibniz algebra has at most two minimal ideals and classify such algebras into three distinct types according to the structure of the socle, extending the classical Lie-theoretic classification. In the solvable case, we obtain an alternative characterisation of primitive Leibniz algebras of type 1 in terms of split extensions by self-centralising minimal ideals.
Source: Mathematics
DOI: 10.3390/math14091531
Author: Zekiye Çiloğlu Şahin
Institution: Süleyman Demirel Üniversitesi
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7160213176
FWCI:
Cites:
Cited by:
Related to: