Skew left braces of nilpotent type

By Ferran Cedó, Agata Smoktunowicz, Leandro Vendramin. Proceedings of the London Mathematical Society, 2018

104 citations recorded by the source corpus.

We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to define left and right nilpotent skew left braces. Several results related to these concepts are proved and applications to infinite left braces are given. Indecomposable solutions of the Yang–Baxter equation are explored using the structure of skew left braces.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6a1b0e2d37451587cc8a41960148d7ab473b964b

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In Algebra and Number Theory

1. Valeriy G. Bardakov
2. Vsevolod Gubarev

In Geometry and Topology

1. Valeriy G. Bardakov
2. Vsevolod Gubarev

Citations in the corpus

• Rota—Baxter groups, skew left braces, and the Yang—Baxter equation (2021, background): “Let us suggest the new version of already known [11] definition of what is a nilpotent left skew brace.”
• Post-groups, (Lie-)Butcher groups and the Yang–Baxter equation (2023, unknown): “The nilpotency and factorization of skew-left braces were investigated in [10, 33].”