English

Extensions of Yang-Baxter sets

Quantum Algebra 2023-06-07 v1 Group Theory

Abstract

The paper extends the notion of braided set and its close relative - the Yang-Baxter set - to the category of vector spaces and explore structure aspects of such a notion as morphisms and extensions. In this way we describe a family of solutions for the Yang-Baxter equation on the product of B and C if given B and C correspond to two linear (set-theoretic) solutions of the Yang-Baxter equation. One of the key observation is the relation of this question with the virtual pure braid group.

Keywords

Cite

@article{arxiv.2206.09629,
  title  = {Extensions of Yang-Baxter sets},
  author = {Valeriy G. Bardakov and Dmitry V. Talalaev},
  journal= {arXiv preprint arXiv:2206.09629},
  year   = {2023}
}

Comments

29 pages, 3 figures

R2 v1 2026-06-24T11:56:59.217Z