TY - JOUR
ID - 60104
T1 - Affine actions and the Yang-Baxter equation
JO - Advances in Operator Theory
JA - AOT
LA - en
SN -
A1 - Yang, Dilian
Y1 - 2018
PY - 2018/07/01
VL - 3
IS - 3
SP - 710
EP - 730
KW - Yang-Baxter equation
KW - set-theoretic solution
KW - affine action
KW - C*-dynamical system
DO - 10.15352/aot.1801-1298
N2 - 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.
UR - http://www.aot-math.org/article_60104.html
L1 - http://www.aot-math.org/pdf_60104_5b1e93d062f80db45bd3e9f530226155.html
ER -