Advances in Operator Theory
- Adv. Oper. Theory
- Volume 3, Number 3 (2018), 710-730.
Affine actions and the Yang–Baxter equation
In this paper, the relations between the Yang–Baxter equation and affine actions are explored in detail. In particular, we classify the injective set-theoretic solutions of the Yang–Baxter equation in two ways: (i) by their associated affine actions of their structure groups on their derived structure groups, and (ii) by the $C^*$-dynamical systems obtained from their associated affine actions. On the way to our main results, several other useful results are also obtained.
Adv. Oper. Theory, Volume 3, Number 3 (2018), 710-730.
Received: 19 January 2018
Accepted: 29 March 2018
First available in Project Euclid: 27 April 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 16T25: Yang-Baxter equations
Secondary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
Yang, Dilian. Affine actions and the Yang–Baxter equation. Adv. Oper. Theory 3 (2018), no. 3, 710--730. doi:10.15352/aot.1801-1298. https://projecteuclid.org/euclid.aot/1524794448