On skew braces and their ideals

A. Konovalov; Agata Smoktunowicz; Leandro Vendramin

doi:10.1080/10586458.2018.1492476

On skew braces and their ideals

A. Konovalov, Agata Smoktunowicz, Leandro Vendramin

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

23 Citations (Scopus)

103 Downloads (Pure)

Abstract

We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series of ideals, prime and semiprime ideals, Baer and Wedderburn radicals and solvability. The paper contains several questions.

Original language	English
Number of pages	10
Journal	Experimental Mathematics
Volume	Latest Articles
Early online date	22 Dec 2018
DOIs	https://doi.org/10.1080/10586458.2018.1492476
Publication status	E-pub ahead of print - 22 Dec 2018

Keywords

Braces
Yang-Baxter equation
Radical rings

Access to Document

10.1080/10586458.2018.1492476

Experimenting_with_braces
© 2018 Taylor & Francis Group, LLC. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at: https://doi.org/10.1080/10586458.2018.1492476
Accepted author manuscript, 310 KB

Cite this

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title = "On skew braces and their ideals",

abstract = "We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series of ideals, prime and semiprime ideals, Baer and Wedderburn radicals and solvability. The paper contains several questions.",

keywords = "Braces, Yang-Baxter equation, Radical rings",

author = "A. Konovalov and Agata Smoktunowicz and Leandro Vendramin",

note = "The first-named author is partially supported by CCP CoDiMa (EP/M022641/1) and the OpenDreamKit Horizon 2020 European Research Infrastructures project (#676541). The second-named author is supported by the ERC Advanced grant 320974. The third-named author is supported by PICT-201-0147, MATH-AmSud 17MATH-01 and ERC Advanced grant 320974.",

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doi = "10.1080/10586458.2018.1492476",

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journal = "Experimental Mathematics",

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AU - Konovalov, A.

AU - Smoktunowicz, Agata

AU - Vendramin, Leandro

N1 - The first-named author is partially supported by CCP CoDiMa (EP/M022641/1) and the OpenDreamKit Horizon 2020 European Research Infrastructures project (#676541). The second-named author is supported by the ERC Advanced grant 320974. The third-named author is supported by PICT-201-0147, MATH-AmSud 17MATH-01 and ERC Advanced grant 320974.

PY - 2018/12/22

Y1 - 2018/12/22

N2 - We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series of ideals, prime and semiprime ideals, Baer and Wedderburn radicals and solvability. The paper contains several questions.

AB - We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series of ideals, prime and semiprime ideals, Baer and Wedderburn radicals and solvability. The paper contains several questions.

KW - Braces

KW - Yang-Baxter equation

KW - Radical rings

UR - https://arxiv.org/abs/1804.04106

U2 - 10.1080/10586458.2018.1492476

DO - 10.1080/10586458.2018.1492476

M3 - Article

SN - 1058-6458

VL - Latest Articles

JO - Experimental Mathematics

JF - Experimental Mathematics

ER -

On skew braces and their ideals

Abstract

Keywords

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Other files and links

Fingerprint

H2020 OPENDREAMKIT: OPENDREAMKIT (partner)

CoDiMa: CoDiMa (CCP in the area of Computational Discrete Mathematics)

Olexandr Konovalov

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.7.0 (GAP package)

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.1.0 (GAP package)

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.0.1 (GAP package)

Cite this

On skew braces and their ideals

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

H2020 OPENDREAMKIT: OPENDREAMKIT (partner)

CoDiMa: CoDiMa (CCP in the area of Computational Discrete Mathematics)

Profiles

Olexandr Konovalov

Datasets

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.7.0 (GAP package)

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.1.0 (GAP package)

YangBaxter - Combinatorial Solutions for the Yang-Baxter equation, Version 0.0.1 (GAP package)

Cite this