Affine cellularity of affine 𝑞-Schur algebras

We first present an axiomatic approach to proving that an algebra with a cell theory in Lusztig’s sense is affine cellular in the sense of Koenig and Xi; then we will show that the affine q q -Schur algebra U r , n , n \mathfrak {U}_{r,n,n} is affine cellular. We also show that U r , n , n \mathfrak {U}_{r,n,n} is of finite global dimension and its derived module category admits a stratification when the parameter v ∈ C ∗ v\in \mathbb {C}^{*} is not a root of unity.