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In this paper, we generalize to the context of algebras some recent resultson the existence of common hypercyclic vectors for families of products ofbackward shift operators. We also give, in a multi-dimensional setting, apositive answer to a question raised by F. Bayart, D. Papathanasiou and theauthor about the existence of a common hypercyclic algebra on$\ell_1(\mathbb{N})$ with the convolution product for the family of backwardshifts $(B_{w(\lambda)})_{\lambda>0}$ induced by the weights$w_n(\lambda)=1+\lambda/n$.

Common hypercyclic algebras for families of products of backward shifts