The deformations of higher-spin symmetries induced by cubic interactions of symmetric massless bosonic fields are analyzed within the metric-like formalism. In particular, we identify a class of couplings which leave the gauge algebra Abelian but deform one (out of three) gauge transformation, and another class of couplings which deform all three gauge transformations in (A)dS but only two in the flat-space limit. The former class is related to higher-spin algebra multiplets (representations of the global algebra). The latter class is what makes (A)dS a distinguished background for higher-spin interactions and includes in particular the gravitational interactions of higher-spin fields, retrospectively accounting for the Fradkin-Vasiliev solution to the Aragone-Deser problem.

Some issues of higher-spin (HS) gauge theory (in d+1>3) related to its cubic interactions and holography are discussed. After providing a very brief overview on the topic, I show how to construct all gauge consistent cubic interactions using the ambient-space formulation. Its number matches that of all possible 3pt functions, recently derived by other groups. However only one vertex corresponds to the free scalar CFT on the boundary, hence the metric-like version of the vertex encoded in Vasiliev's equation.