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 -ary operations, “braces”.
Definition
A left brace is left truss which is an Abelian group under its multiplicative operation.
Literature
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