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An explicit product for the on-shell higher-spin algebra in $AdS_d$-space
For $d>3$ we construct the product of the bosonic on-shell higher-spin algebra directly on the AdS-traceless representatives. We find the traceless projector in closed form, determine all linear relations among the trace-producing operators, and prove that every class modulo the $\mathfrak{sp}(2)$ i
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