Tensor products of higher APR tilting modules

TL;DR

This paper investigates the behavior of higher APR and BB tilting modules under tensor products, demonstrating that such tensor products preserve the tilting module structure within higher Auslander-Reiten theory.

Contribution

It proves that tensor products of higher APR and BB tilting modules result in modules of the same type, extending the understanding of tilting modules in higher Auslander-Reiten theory.

Findings

Tensor product of higher APR tilting modules is a higher APR tilting module.

Tensor product of higher BB tilting modules is a higher BB tilting module.

Preservation of tilting module properties under tensor products.

Abstract

The higher APR tilting modules and higher BB tilting modules were introduced and studied in higher Auslander-Reiten theory. Our objective is to consider these tilting modules by the corresponding simple modules, and show that the tensor product of higher APR (BB) tilting modules is a higher APR (BB) tilting module.