Study on the Group-Theoretic and Ring-Theoretic Properties of the Centroid of a Class of Filiform Lie Algebras

Demin Yu and Zihao Zhong

Journal of Mathematics, 2026, vol. 2026, 1-11

Abstract: This paper investigates the centroid structure and algebraic properties of a class of n-dimensional filiform Lie algebras Ln. The structural characteristics of the group G and the ring R formed by centroids are analyzed. The invertible linear transformations of the centroid form a mixed group G, and it is proved that G can be decomposed into the internal direct product of two commuting subgroups G1 and G2, where G2 is a torsion-free group. The centroid ring R is a commutative ring with a unit element and a zero-divisor if and only if the element on the main diagonal is zero. By constructing a ring homomorphism Ψ:R⟶R1, it is proved that ker Ψ is a maximal ideal of R, and all its nonzero elements are zero-divisors.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/3198919.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/3198919.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3198919

DOI: 10.1155/jom/3198919

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().