#### Vol. 292, No. 1, 2018

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Cellular structures using $\boldsymbol{U}_q$-tilting modules

### Henning Haahr Andersen, Catharina Stroppel and Daniel Tubbenhauer

Vol. 292 (2018), No. 1, 21–59
##### Abstract

We use the theory of ${U}_{q}$-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group ${U}_{q}$ attached to a Cartan matrix and include the nonsemisimple cases for $q$ being a root of unity and ground fields of positive characteristic. Our approach also generalizes to certain categories containing infinite-dimensional modules. As applications, we give a new semisimplicity criterion for centralizer algebras, and we recover the cellularity of several known algebras (with partially new cellular bases) which all fit into our general setup.

##### Keywords
cellular algebras, cellular bases, tilting modules, quantum enveloping algebras
##### Mathematical Subject Classification 2010
Primary: 17B10, 17B37, 20G05
Secondary: 16S50, 20C08, 20G42