arXiv:1211.6979v2 [hep-th] 29 Dec 2012 Non-abelian cubic vertices for higher-spin fields in AdS d Nicolas Boulanger 1 , Dmitry Ponomarev 2 and E.D. Skvortsov 3 1,2 Universit´ e de Mons – UMONS, 20 Place du Parc, 700 Mons, Belgium 3 Albert Einstein Institute, Golm, Germany, D-14476, Am M¨ uhlenberg 1 3 Lebedev Institute of Physics, Moscow, Russia, 119991, Leninsky pr-t, 53 Abstract We use the Fradkin-Vasiliev procedure to construct the full set of non-abelian cubic vertices for totally symmetric higher spin gauge fields in AdS d space. The number of such vertices is given by a certain tensor-product multiplicity. We discuss the one-to-one relation between our result and the list of non-abelian gauge deformations in flat space obtained elsewhere via the cohomological approach. We comment about the uniqueness of Vasiliev’s simplest higher-spin algebra in relation with the (non)associativity properties of the gauge algebras that we classified. The gravitational interactions for (partially)-massless (mixed)-symmetry fields are also discussed. We also argue that those mixed-symmetry and/or partially-massless fields that are described by one-form connections within the frame-like approach can have nonabelian interactions among themselves and again the number of nonabelian vertices should be given by tensor product multiplicities. 1 Research Associate of the Fund for Scientific Research-FNRS (Belgium); nicolas.boulanger@umons.ac.be 2 dmitri.ponomarev@umons.ac.be 3 skvortsov@lpi.ru