Higher APR tilting preserves n-representation infiniteness

We show that m-APR tilting preserves n  -representation infiniteness for 1≤m≤n1≤m≤n. Moreover, we show that these tilting modules lift to tilting modules for the corresponding higher preprojective algebras, which is (n+1)(n+1)-CY algebras. We also study the interplay of the two kinds of tilting modules.