HNN-extensions of Leibniz algebras

Manuel Ladra; Mohammad Shahryari; Chia Zargeh

doi:10.1016/j.jalgebra.2019.05.014

HNN-extensions of Leibniz algebras

Manuel Ladra^*, Mohammad Shahryari, Chia Zargeh

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

In this paper we construct HNN-extensions of diassociative algebras and Leibniz algebras and prove that every Leibniz algebra embeds into any of its HNN-extensions. We also prove that every Leibniz algebra with at most countable dimension embeds into a two-generator Leibniz algebra.

Original language	English
Pages (from-to)	183-200
Number of pages	18
Journal	Journal of Algebra
Volume	532
DOIs	https://doi.org/10.1016/j.jalgebra.2019.05.014
Publication status	Published - Aug 15 2019

Keywords

Composition lemma
Dialgebras
Gröbner-Shirshov bases
HNN-extensions
Leibniz algebras

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2019.05.014

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title = "HNN-extensions of Leibniz algebras",

abstract = "In this paper we construct HNN-extensions of diassociative algebras and Leibniz algebras and prove that every Leibniz algebra embeds into any of its HNN-extensions. We also prove that every Leibniz algebra with at most countable dimension embeds into a two-generator Leibniz algebra.",

keywords = "Composition lemma, Dialgebras, Gr{\"o}bner-Shirshov bases, HNN-extensions, Leibniz algebras",

author = "Manuel Ladra and Mohammad Shahryari and Chia Zargeh",

note = "Funding Information: The first and third authors were partially supported by Agencia Estatal de Investigaci{\'o}n (Spain), grant MTM2016-79661-P (European FEDER support included, UE). Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

month = aug,

day = "15",

doi = "10.1016/j.jalgebra.2019.05.014",

language = "English",

volume = "532",

pages = "183--200",

journal = "Journal of Algebra",

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T1 - HNN-extensions of Leibniz algebras

AU - Ladra, Manuel

AU - Shahryari, Mohammad

AU - Zargeh, Chia

N1 - Funding Information: The first and third authors were partially supported by Agencia Estatal de Investigación (Spain), grant MTM2016-79661-P (European FEDER support included, UE). Publisher Copyright: © 2019 Elsevier Inc.

PY - 2019/8/15

Y1 - 2019/8/15

N2 - In this paper we construct HNN-extensions of diassociative algebras and Leibniz algebras and prove that every Leibniz algebra embeds into any of its HNN-extensions. We also prove that every Leibniz algebra with at most countable dimension embeds into a two-generator Leibniz algebra.

AB - In this paper we construct HNN-extensions of diassociative algebras and Leibniz algebras and prove that every Leibniz algebra embeds into any of its HNN-extensions. We also prove that every Leibniz algebra with at most countable dimension embeds into a two-generator Leibniz algebra.

KW - Composition lemma

KW - Dialgebras

KW - Gröbner-Shirshov bases

KW - HNN-extensions

KW - Leibniz algebras

UR - http://www.scopus.com/inward/record.url?scp=85066480002&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066480002&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2019.05.014

DO - 10.1016/j.jalgebra.2019.05.014

M3 - Article

AN - SCOPUS:85066480002

SN - 0021-8693

VL - 532

SP - 183

EP - 200

JO - Journal of Algebra

JF - Journal of Algebra

ER -

HNN-extensions of Leibniz algebras

Abstract

Keywords

ASJC Scopus subject areas

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