Advances in Operator Theory

Affine actions and the Yang–Baxter equation

Dilian Yang

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‎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.

Article information

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

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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–Baxter equation ‎set-theoretic solution‎ ‎affine action ‎‎$C^*$-dynamical system


Yang, Dilian. Affine actions and the Yang–Baxter equation. Adv. Oper. Theory 3 (2018), no. 3, 710--730. doi:10.15352/aot.1801-1298.

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