中文

Set-theoretical solutions to the quantum Yang-Baxter equation

量子代数 2025-11-20 v2

摘要

In 1992 V..Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions to the quantum Yang-Baxter equation, i.e. solutions given by a permutation R of the set X×XX\times X, where X is a fixed set. In this paper we study such solutions, which in addition satisfy the unitarity and nondegeneracy conditions. We discuss the geometric and algebraic interpretations of such solutions, introduce several constructions of them, and make first steps towards their classification.

关键词

引用

@article{arxiv.math/9801047,
  title  = {Set-theoretical solutions to the quantum Yang-Baxter equation},
  author = {Pavel Etingof and Travis Schedler and Alexandre Soloviev},
  journal= {arXiv preprint arXiv:math/9801047},
  year   = {2025}
}

备注

36 pages, amstex, figures, revised and expanded, contains q-alg/9707027 as a small subset