Affine cellularity of affine $q$-Schur algebras
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- by Weideng Cui
- Proc. Amer. Math. Soc. 144 (2016), 4663-4672
- DOI: https://doi.org/10.1090/proc/13261
- Published electronically: July 22, 2016
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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.References
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Bibliographic Information
- Weideng Cui
- Affiliation: School of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China
- MR Author ID: 1107028
- Email: cwdeng@amss.ac.cn
- 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
- Communicated by: Pham Huu Tiep
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4663-4672
- MSC (2010): Primary 20G43; Secondary 16E10, 20G05
- DOI: https://doi.org/10.1090/proc/13261
- MathSciNet review: 3544518
Dedicated: Dedicated to Professor George Lusztig on his seventieth birthday