Higher APR tilting preserves $n$-representation infiniteness

TL;DR

This paper proves that higher APR tilting maintains $n$-representation infiniteness and explores their role in higher preprojective algebras, revealing new relationships in $(n+1)$-CY algebras.

Contribution

It demonstrates that $m$-APR tilting preserves $n$-representation infiniteness and introduces new tilting modules for higher preprojective algebras.

Findings

$m$-APR tilting preserves $n$-representation infiniteness

Provides different tilting modules for higher preprojective algebras

Explores the interplay between two types of tilting modules

Abstract

We show that $m$-APR tilting preserves $n$-representation infiniteness for $1\leq m\leq n$. Moreover, we show that these tilting modules provide different tilting modules for the corresponding higher preprojective algebras, which is $(n+1)$-CY algebras. We also study the interplay of the two kinds of tilting modules.