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Affine cellularity of affine $ q$-Schur algebras


Author: Weideng Cui
Journal: Proc. Amer. Math. Soc. 144 (2016), 4663-4672
MSC (2010): Primary 20G43; Secondary 16E10, 20G05
DOI: https://doi.org/10.1090/proc/13261
Published electronically: July 22, 2016
MathSciNet review: 3544518
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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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Additional Information

Weideng Cui
Affiliation: School of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China
Email: cwdeng@amss.ac.cn

DOI: https://doi.org/10.1090/proc/13261
Keywords: Affine cellular algebras, affine $q$-Schur algebras, finite global dimension
Received by editor(s): October 1, 2014
Received by editor(s) in revised form: August 16, 2015, and January 17, 2016
Published electronically: July 22, 2016
Dedicated: Dedicated to Professor George Lusztig on his seventieth birthday
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2016 American Mathematical Society