2024/04/22 by I. G. Korepanov, Korepanov, Igor G.
Computer Science · #15A24 (Primary) #82B20 #82B23 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2404.13913
openalex publication_date 2024/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this short note, we construct solutions to quantum tetrahedron equation of the kind "with variables on the edges". Each of these variables takes just two values, called sometimes "colors". We propose two different constructions. The first of them involves, in particular, two \mathcal R-operators each depending on one parameter, while these parameters are independent from each other; the number of nonvanishing matrix entries in these two \mathcal R-operators is either 12 or 14. In the second construction, we use what may be called "modified tetrahedron in a direct sum" to produce, again, quantum tetrahedron solutions. All matrix entries of our \mathcal R-operators are nonnegative, if the relevant parameters are chosen properly.