I'm studying Lie bialgebras: https://en.wikipedia.org/wiki/Lie_bialgebra.
I'm a bit confused about the way of writing the so called "dual Jacobi identity".
On Majid's book "a Quantum group Primer" it is written as $$\tag{1} (\delta \otimes 1 )\circ \delta (X_i) + cyclic =0,\,\,\,\,\,X_i \in g $$where $\delta:g \to g\otimes g $ is the skew symmetric co-commutator map, $g$ a Lie algebra.
My question is very simple: what is "$+cyclic$" in (1)? I understand the basis dependent identity but I'm unable to write down the other 2 bits in the basis independent version.. I guess one is simply: $(1 \otimes \delta )\circ \delta (X_i)$ but what can one rotate next? (1) needs to be applied to a single Lie algebra element $X$..
Thank you!