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Summer 2018 Affine actions and the Yang–Baxter equation
Dilian Yang
Adv. Oper. Theory 3(3): 710-730 (Summer 2018). DOI: 10.15352/aot.1801-1298

Abstract

‎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.

Citation

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Dilian Yang. "Affine actions and the Yang–Baxter equation." Adv. Oper. Theory 3 (3) 710 - 730, Summer 2018. https://doi.org/10.15352/aot.1801-1298

Information

Received: 19 January 2018; Accepted: 29 March 2018; Published: Summer 2018
First available in Project Euclid: 27 April 2018

zbMATH: 06902463
MathSciNet: MR3795111
Digital Object Identifier: 10.15352/aot.1801-1298

Subjects:
Primary: 16T25
Secondary: 46L55

Keywords: ‎‎$C^*$-dynamical system , affine action , ‎set-theoretic solution‎ , Yang–Baxter equation

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 3 • Summer 2018
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