Involutive Yang-Baxter Groups
Ferran Cedo, Eric Jespers, Angel del Rio

TL;DR
This paper explores the classification of involutive Yang-Baxter (IYB) groups, which correspond to solutions of the Yang-Baxter equation, and introduces methods to construct infinitely many groups of I-type with specific IYB groups.
Contribution
It provides new results supporting the conjecture that all IYB groups are solvable and introduces a method to construct infinitely many I-type groups with a given IYB group.
Findings
Some classes of groups are proven to be IYB groups.
A non-obvious construction method for infinitely many I-type groups is presented.
The paper supports the conjecture that all IYB groups are solvable.
Abstract
In 1992 Drinfeld posed the question of finding the set theoretic solutions of the Yang-Baxter equation. Recently, Gateva-Ivanova and Van den Bergh and Etingof, Schedler and Soloviev have shown a group theoretical interpretation of involutive non-degenerate solutions. Namely, there is a one-to-one correspondence between involutive non-degenerate solutions on finite sets and groups of -type. A group of -type is a group isomorphic to a subgroup of the natural semidirect product of , the free abelian group of rank , by , the symmetric group on letters, so that the projection onto is a bijective map. The projection of onto we call an involutive Yang-Baxter group (IYB group). This suggests the following strategy to attack Drinfeld's problem for involutive non-degenerate set theoretic solutions. First classify the IYB groups…
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras · Advanced Algebra and Logic
