Page 99 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 99
NCOMMUTATIVE STRUCTURES WITHIN ORDER STRUCTURES, SEMIGROUPS
AND UNIVERSAL ALGEBRA (MS-67)
Skew lattices and set-theoretic solutions of the Yang-Baxter equation
Charlotte Verwimp, cverwimp@vub.be
Vrije Universiteit Brussel, Belgium
The Yang-Baxter equation originates from papers by Yang and Baxter on quantum and statistical
mechanics, and the search for solutions has attracted numerous studies both in mathematical
physics and pure mathematics. As the study of arbitrary solutions is complex, Drinfeld proposed
in 1992 to focus on the class of set-theoretic solutions. The goal is simple, find all set-theoretic
solutions of the Yang-Baxter equation.
Recently introduced algebraic structures, like braces, cycle sets and their generalizations, are
related to special classes of set-theoretic solutions. Still, an algebraic structure that describes
all set-theoretic solutions of the Yang-Baxter equation is not known. In this talk, we discuss
set-theoretic solutions obtained from skew lattices, an algebraic structure that had not yet been
related to the Yang-Baxter equation. Such solutions are degenerate in general, and thus different
from solutions obtained from braces and other structures.
This talk is based on joint work with Karin Cvetko-Vah.
97
AND UNIVERSAL ALGEBRA (MS-67)
Skew lattices and set-theoretic solutions of the Yang-Baxter equation
Charlotte Verwimp, cverwimp@vub.be
Vrije Universiteit Brussel, Belgium
The Yang-Baxter equation originates from papers by Yang and Baxter on quantum and statistical
mechanics, and the search for solutions has attracted numerous studies both in mathematical
physics and pure mathematics. As the study of arbitrary solutions is complex, Drinfeld proposed
in 1992 to focus on the class of set-theoretic solutions. The goal is simple, find all set-theoretic
solutions of the Yang-Baxter equation.
Recently introduced algebraic structures, like braces, cycle sets and their generalizations, are
related to special classes of set-theoretic solutions. Still, an algebraic structure that describes
all set-theoretic solutions of the Yang-Baxter equation is not known. In this talk, we discuss
set-theoretic solutions obtained from skew lattices, an algebraic structure that had not yet been
related to the Yang-Baxter equation. Such solutions are degenerate in general, and thus different
from solutions obtained from braces and other structures.
This talk is based on joint work with Karin Cvetko-Vah.
97
