Lie algebras for multiple Eisenstein series and multiple q-zeta values

Racinet's double shuffle Lie algebra $\mathfrak{dm}_0$ encodes the double shuffle relations of multiple zeta values. We study two analogues of $\mathfrak{dm}_0$ for multiple Eisenstein series and $q$-analogues of multiple zeta values, namely the space $\operatorname{BARI}_{\operatorname{swap},\mathr