Abstract
We consider a multitude of topics in mathematics where unification constructions play an important role: the Yang–Baxter equation and its modified version, Euler’s formula for dual numbers, means and their inequalities, topics in differential geometry, etc. It is interesting to observe that the idea of unification (unity and union) is also present in poetry. Moreover, Euler’s identity is a source of inspiration for the post-modern poets.
Highlights
The Yang–Baxter equation, sometimes denoted as QYBE [1,2,3,4,5], has many applications in physics, quantum groups, knot theory, quantum computers, logic, etc
Finding solutions to the colored Yang–Baxter equation is a very important and difficult problem, and we present interesting solutions in this paper
This equation is a type of Yang–Baxter matrix equation, it is related to the three matrix problem, and it can be interpreted as “a generalized eigenvalue problem”
Summary
The Yang–Baxter equation, sometimes denoted as QYBE [1,2,3,4,5], has many applications in physics, quantum groups, knot theory, quantum computers, logic, etc. Finding solutions to the colored Yang–Baxter equation is a very important and difficult problem, and we present interesting solutions in this paper. These solutions appeared as a consequence of a unifying point of view on some of the most beautiful equations in mathematics [7]. We refer to Euler’s formulas for dual numbers, which can be related to the colored Yang–Baxter equation. We present a unification for the classical means (which unify their inequalities as well). These can be seen as interpolations of means with functions without singularities. We write I for the identity matrix in M4 (k ), respectively, I 0 for the identity matrix in M2 (k )
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