nLab brace

This entry is about an algebraic structure of brace stemming from the study of set-theoretic Yang-Baxter equation. See entry brace algebra for another algebraic structure, with nn-ary operations, “braces”.


A left brace is left truss which is an Abelian group under its multiplicative operation.


  • W. Rump, Braces, radical rings, and the quantum Yang-Baxter equation, J. Algebra 307 (2007), no. 1, 153-170
  • Wolfgang Rump, Generalized radical rings, unknotted biquandles, and quantum groups, Colloquium Mathematicum 109 (2007), 85-100 doi
  • W. Rump, The brace of a classical group, Note di Matematica 34 (2014) n.1, 115-144 pdf
  • W. Rump, Construction of finite braces, Ann. Comb. 23, 391–416 (2019) doi
  • F. Cedó, E. Jespers, J. Okniński, Braces and the Yang–Baxter equation, Commun. Math. Phys. 327, 101–116 (2014). doi
category: algebra

Last revised on May 26, 2023 at 07:54:57. See the history of this page for a list of all contributions to it.