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

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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
Additional Information:
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
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Deposited On:
03 Nov 2022 17:05
Last Modified:
22 Nov 2022 11:05