On tensor products of path algebras of type A

We derive a formula for the Coxeter polynomial of the s  -fold tensor product ⨂i=1sF[A→ni−1] of path algebras of linearly oriented quivers of Dynkin type Ani−1Ani−1, in terms of the weights n1,…,ns≥2n1,…,ns≥2, and show that conversely the weights can be recovered from the Coxeter polynomial of the tensor product. Our results have relevance in singularity theory, in particular these algebras occur as endomorphism algebras of tilting objects in certain stable categories of vector bundles.