Translator Disclaimer
2019 Leibniz algebras with low-dimensional maximal Lie quotients
William J. Cook, John Hall, Vicky W. Klima, Carter Murray
Involve 12(5): 839-853 (2019). DOI: 10.2140/involve.2019.12.839

Abstract

Every Leibniz algebra has a maximal homomorphic image that is a Lie algebra. We classify cyclic Leibniz algebras over an arbitrary field. Such algebras have the 1-dimensional abelian Lie algebra as their maximal Lie quotient. We then give examples of Leibniz algebras whose associated maximal Lie quotients exhaust all 2-dimensional possibilities.

Citation

Download Citation

William J. Cook. John Hall. Vicky W. Klima. Carter Murray. "Leibniz algebras with low-dimensional maximal Lie quotients." Involve 12 (5) 839 - 853, 2019. https://doi.org/10.2140/involve.2019.12.839

Information

Received: 31 August 2018; Revised: 9 October 2018; Accepted: 1 January 2019; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07072549
MathSciNet: MR3954299
Digital Object Identifier: 10.2140/involve.2019.12.839

Subjects:
Primary: 17A32
Secondary: 17A60

Keywords: cyclic Leibniz algebra , Leibniz algebra , low-dimensional examples

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 5 • 2019
MSP
Back to Top