Groups, radical rings, and the Yang-Baxter equation : a combinatorial approach to solutions / Ferran Cedó, Leandro Vendramin.

Format:

Book

Author/Creator:

Cedó, Ferran, Author.

Vendramin, Leandro, Author.

Series:

Progress in mathematics (Boston, Mass.) ; 2296-505X 361.

Progress in mathematics, 0743-1643 ; volume 361

Language:

English

Subjects (All):

Group theory.

Set theory.

Yang-Baxter equation.

Physical Description:

xii, 298 pages ; 25 cm

Place of Publication:

Cham : Birkhäuser, Springer Nature Switzerland, [2026]

Summary:

"This monograph provides the first comprehensive introduction to set-theoretic solutions of the Yang-Baxter equation and their deep connections with skew braces. In recent decades, set-theoretic solutions have emerged as an accessible yet rich domain of study, offering new algebraic structures and revealing unexpected connections between seemingly distant fields. A key breakthrough in this direction was the discovery of braces by Rump and the later generalization to skew braces, which provide an elegant algebraic framework for understanding and constructing set-theoretic solutions. This book offers a self-contained, structured, and pedagogically motivated treatment of the subject. Each chapter ends with a list of exercises to work on the presented topics, some open problems, and comments on the authorship and development of the results presented."-- Provided by publisher.

Contents:

Introduction

Preliminaries

The Jacobson Radical

The Yang-Baxter Equation

Nilpotent Groups

Solvable Groups

Complements

Skew Braces

The Structure Skew Brace of a Solution

Bierbach Groups

Garside Groups

Left Nilpotent Skew Braces

Right Nilpotent Skew Braces

Multipermutation Solutions

Factorizations

Transitive Groups

Involutive Solutions

Simple Skew Braces.

Notes:

Includes bibliographical references (pages 287-291) and index.

Other Format:

Online version: Cedó, Ferran. Groups, radical rings, and the Yang-Baxter equation.

ISBN:

9783032015235

3032015235

OCLC:

1574167998

Publisher Number:

9783032015235