Introduction to the Yang-Baxter equation with open problems.
type: Item
instance of: scholarly article
title: Introduction to the Yang-Baxter equation with open problems.
zbMATH Open document ID: 1293.16027
published in: Axioms
publication date: 2014-08-15T00:00:00Z
review text: Summary: The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C. N. Yang, and in statistical mechanics, in R. J. Baxter's work. Later, it turned out that this equation plays a crucial role in: quantum groups, knot theory, braided categories, analysis of integrable systems, quantum mechanics, non-commutative descent theory, quantum computing, non-commutative geometry, etc. Many scientists have found solutions for the Yang-Baxter equation, obtaining qualitative results (using the axioms of various algebraic structures) or quantitative results (usually using computer calculations). However, the full classification of its solutions remains an open problem. In this paper, we present the (set-theoretical) Yang-Baxter equation, we sketch the proof of a new theorem, we state some problems, and discuss about directions for future research.
Mathematics Subject Classification ID: 16T25
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 6330786
zbMATH Keywords: set-theoretical Yang-Baxter equation
zbMATH Keywords: algebra structures
zbMATH Keywords: Hopf algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: relations on sets
author: Florin F. Nichita
MaRDI profile type: Publication
full work available at URL: axioms1010033
OpenAlex ID: W2073669412
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DOI: 10.3390/AXIOMS1010033
description: scientific article; zbMATH DE number 6330786