Abstract
Yang–Baxter operators from algebra structures appeared for the first time in [Citation11, Citation22, Citation23]. Later, Yang–Baxter systems from entwining structures were constructed in [Citation8]. In fact, Yang–Baxter systems are equivalent with braid systems. In this paper we show that braidings and entwinings of various algebraic structures—in particular, algebra factorisations—can be constructed from a braid system, whence from a Yang–Baxter system as well.
ACKNOWLEDGMENTS
The authors would like to thank the referee for carefully reading the manuscript, making valuable comments, and suggesting a first version of Lemma 3.1.
Notes
Communicated by T. Albu.