From Braces to Hecke algebras & Quantum Groups

Abstract

We examine links between the theory of braces and set theoretical solutions of the Yang-Baxter equation, and fundamental concepts from the theory of quantum integrable systems. More precisely, we make connections with Hecke algebras and we identify new quantum groups associated to set-theoretic solutions coming from braces. We also construct a novel class of quantum discrete integrable systems and we derive symmetries for the corresponding periodic transfer matrices.

25 pages, LaTex. Clarifying comments added, a few typos corrected. E-pub ahead of print in: Journal of Algebra and its Applications

References in corpus (8)

• Semigroups of I-type
• Factorizations of skew braces
• Set theoretic Yang-Baxter & reflection equations and quantum group symmetries
• The retraction relation for biracks
• On skew braces and their ideals (with an Appendix by Agata Smoktunowicz)
• A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation
• An Associative Left Brace is a Ring
• Murphy elements from the double-row transfer matrix

Cited by in corpus (6)

• Set theoretic Yang-Baxter equation, braces and Drinfeld twists
• Algebraic approach to Rump's results on relations between braces and pre-Lie algebras
• Near braces and p-deformed braided groups
• Discretizations of the generalized AKNS scheme
• Novel non-involutive solutions of the Yang-Baxter equation from (skew) braces
• Integrable extensions of Adler's map via Grassmann algebras