Affine cellularity of affine 𝑞-Schur algebras

Cui, Weideng

doi:10.1090/proc/13261

Affine cellularity of affine $q$-Schur algebras
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Proc. Amer. Math. Soc. 144 (2016), 4663-4672 Request permission

Abstract:

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 $q$-Schur algebra $\mathfrak {U}_{r,n,n}$ is affine cellular. We also show that $\mathfrak {U}_{r,n,n}$ is of finite global dimension and its derived module category admits a stratification when the parameter $v\in \mathbb {C}^{*}$ is not a root of unity.

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