Question on a paper by Shnider and Sternberg

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I'm reading the paper 'The cobar resolution and a restricted deformation theory' by S. Shnider and S. Sternberg. I do not understand the definition of the map $\delta_p$ defined in section $3$. The problem is that I'm unsure on what is meant by $\text{Ad}(\Psi_{i,p+1})$. I've looked at their book 'Quantum groups' and on page $20$ the letters $\text{Ad}$ are also used, but very differently. Other than that it is quite clear what the intention of the paper is.