Tensor Products and Higher Auslander-reiten Theory

Article history: Received 8 July 2015 Received in revised form 22 February 2016 Available online 4 August 2016 Communicated by S. Koenig We investigate how the higher almost split sequences over a tensor product of algebras are related to those over each factor. Herschend and Iyama give in [6] a 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. © 2016 Elsevier B.V. All rights reserved.