Groups, Radical Rings, and the Yang-Baxter Equation : A Combinatorial Approach to Solutions / by Ferran Cedó, Leandro Vendramin.

Format:

Book

Author/Creator:

Cedó, Ferran.

Series:

Progress in Mathematics, 2296-505X ; 361

Language:

English

Subjects (All):

Associative rings.

Associative algebras.

Group theory.

Mathematical physics.

Associative Rings and Algebras.

Group Theory and Generalizations.

Mathematical Physics.

Local Subjects:

Associative Rings and Algebras.

Group Theory and Generalizations.

Mathematical Physics.

Physical Description:

1 online resource (517 pages)

Edition:

1st ed. 2026.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 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. The primary audience consists of researchers and advanced graduate students working on or entering topics related to the Yang–Baxter equation, especially those with interests in algebra, set-theoretic solutions, and skew braces theory. Given its self-contained nature, the book is also suitable for graduate students seeking a pathway into current research, as it provides foundational material alongside recent developments.

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:

Description based on publisher supplied metadata and other sources.

ISBN:

3-032-01524-3

9783032015242

OCLC:

1572210923