Cubic Interactions of Bosonic Higher Spin Gauge Fields in $AdS_5$

The dynamics of totally symmetric free massless higher spin fields in $AdS_d$ is reformulated in terms of the compensator formalism for AdS gravity. The $AdS_5$ higher spin algebra is identified with the star product algebra with the $su(2,2)$ vector (i.e., $o(4,2)$ spinor) generating elements. Cubic interactions of the totally symmetric bosonic higher spin gauge fields in $AdS_5$, including the interaction with gravity, are formulated at the action level.