We first present an axiomatic approach to proving that an algebra with a cell theory in Lusztigâs 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
â
C
â
v\in \mathbb {C}^{*}
is not a root of unity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citationsâcitations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.