On tensor products of path algebras of type A

Lutz Hille; Jürgen Müller

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arXiv · 1206.1152

On tensor products of path algebras of type A

Lutz Hille·Jürgen Müller

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Abstract

We derive a formula for the Coxeter polynomial of the s-fold tensor product F[A_{n_1-1}] x ... x F[A_{n_s-1}] of path algebras of linearly oriented quivers of Dynkin type A_{n_i-1}, in terms of the weights n_1, ..., n_s > 1, and show that conversely the weights can be recovered from the Coxeter polynomial of the tensor product. Our results have applications in singularity theory, in particular these algebras occur as endomorphism algebras of tilting objects in certain stable categories of vector bundles.

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BibTeX RIS

Lutz Hille, Jürgen Müller. 2012-06-06. On tensor products of path algebras of type A. https://arxiv.org/abs/1206.1152

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