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We analyze asymptotic symmetry algebras in (2+1)-dimensional non-AdShigher-spin gravity with a focus on AdS$_2\times\mathbb{R}$ and$\mathbb{H}_2\times\mathbb{R}$. We find a consistent set of boundary conditionsfor spin-3 gravity in the non-principal embedding and calculate thecorresponding asymptotic symmetry algebra in the classical and quantummechanical case. In addition, we check for unitary representations of theresulting quantum $\mathcal{W}_3^{(2)}$ algebra and give an interpretation ofthe corresponding CFT.

Asymptotic Symmetry Algebras in Non-Anti-de-Sitter Higher-Spin Gauge Theories