The structure of biquandle brackets

In their paper entitled “Quantum Enhancements and Biquandle Brackets”, Nelson, Orrison, and Rivera introduced biquandle brackets, which are customized skein invariants for biquandle-colored links. We prove herein that if a biquandle bracket [Formula: see text] is the pointwise product of the pair of functions [Formula: see text] with a function [Formula: see text], then [Formula: see text] is also a biquandle bracket if and only if [Formula: see text] is a biquandle 2-cocycle (up to a constant multiple). As an application, we show that a new invariant introduced by Yang factors in this way, which allows us to show that the new invariant is in fact equivalent to the Jones polynomial on knots. Additionally, we provide a few new results about the structure of biquandle brackets and their relationship with biquandle 2-cocycles.