We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama gave a precise criterion for when the tensor product of an $n$-representation finite algebra and an $m$-representation finite algebra is $(n+m)$-representation finite. In this case we give a complete description of the higher almost split sequences over the tensor product by expressing every higher almost split sequence as the mapping cone of a suitable chain map and using a natural notion of tensor product for chain maps.
On the number of terms in the middle of almost split sequences over cycle-finite artin algebras
Tensor products and intertwining operators for uniserial representations of the Lie algebra $\mathfrak{sl}(2)\ltimes V(m)$
Categorifying the tensor product of a level 1 highest weight and perfect crystal in type A
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