We gratefully acknowledge support from
the Simons Foundation and member institutions.
Full-text links:

Download:

Current browse context:

math.QA

Change to browse by:

References & Citations

Bookmark

(what is this?)
CiteULike logo BibSonomy logo Mendeley logo del.icio.us logo Digg logo Reddit logo

Mathematics > Quantum Algebra

Title: Solutions to quantum tetrahedron equation with two colors and nonnegative matrix entries

Abstract: 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.
Comments: 9 pages; v2: one more construction added
Subjects: Quantum Algebra (math.QA); Mathematical Physics (math-ph)
MSC classes: 15A24 (Primary), 82B20, 82B23
Cite as: arXiv:2404.13913 [math.QA]
  (or arXiv:2404.13913v2 [math.QA] for this version)

Submission history

From: Igor Korepanov [view email]
[v1] Mon, 22 Apr 2024 06:51:11 GMT (5kb)
[v2] Thu, 9 May 2024 04:54:30 GMT (6kb)

Link back to: arXiv, form interface, contact.