# Abelian subalgebras and ideals of maximal dimension in Zinbiel algebras

Ceballos, Manuel and Towers, David (2022) Abelian subalgebras and ideals of maximal dimension in Zinbiel algebras. Communications in Algebra. ISSN 0092-7872

Text (Zinbiel abelian sub ideal_3)
Zinbiel_abelian_sub_ideal_3.pdf - Accepted Version
Restricted to Repository staff only until 20 October 2023.

## Abstract

In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Zinbiel algebras. We study Zinbiel algebras containing maximal abelian subalgebras of codimension $1$ and supersolvable Zinbiel algebras in which such subalgebras have codimension $2$, and we also analyze the case of filiform Zinbiel algebras. We give examples to clarify some results, including listing the values for $\alpha$ and $\beta$ for the low dimensional Zinbiel algebras over the complex field that have been classified.

Item Type:
Journal Article
Journal or Publication Title:
Communications in Algebra
This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 20/10/2022, available online: https://www.tandfonline.com/doi/full/10.1080/00927872.2022.2134409
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2602
Subjects:
Departments:
ID Code:
178575
Deposited By:
Deposited On:
03 Nov 2022 17:05
Refereed?:
Yes
Published?:
Published