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Algebra Structures Arising from Yang–Baxter Systems

Yang–Baxter operators from algebra structures appeared for the first time in [11, 22, 23]. Later, Yang–Baxter systems from entwining structures were constructed in [8]. 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.