On the Colored and the Set-Theoretical Yang–Baxter Equations

This paper is related to several articles published in AXIOMS, SCI, etc. The main concepts of the current paper are the colored Yang–Baxter equation and the set-theoretical Yang–Baxter equation. The Euler formula, colagebra structures, and means play an important role in our study. We show that some...

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Bibliographic Details
Published inAxioms Vol. 10; no. 3; p. 146
Main Authors Iantovics, Laszlo Barna, Nichita, Florin Felix
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2021
Subjects
(colored) Yang–Baxter equation
artificial intelligence (AI)
Axioms
classical means inequalities
coalgebra structures
Euler’s formula
Formulas (mathematics)
Jargon
Mathematical analysis
Operators (mathematics)
Physics
set-theoretical Yang–Baxter equation
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Summary:This paper is related to several articles published in AXIOMS, SCI, etc. The main concepts of the current paper are the colored Yang–Baxter equation and the set-theoretical Yang–Baxter equation. The Euler formula, colagebra structures, and means play an important role in our study. We show that some new solutions for a certain system of equations lead to colored Yang–Baxter operators, which are related to an Euler formula for matrices, and the set-theoretical solutions to the Yang–Baxter equation are related to means. A new coalgebra is obtained and studied.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms10030146