2022/07/29 by Peter Fiebig, Fiebig, Peter
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2207.14516
openalex publication_date 2022/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that tilting modules for quantum groups over local Noetherian domains exist and that the indecomposable tilting modules are parametrized by their highest weight. For this we introduce a model category \mathcal X=\mathcal X\mathscr A(R) associated with a Noetherian \mathbb Z[v,v-1]-domain \mathscr A and a root system R. We show that if \mathscr A is of quantum characteristic 0, the model category contains all U\mathscr A-modules that admit a Weyl filtration. If \mathscr A is in addition local, we study torsion phenomena in the model category. This leads to a construction of torsion free objects in \mathcal X. We show that these correspond to tilting modules for the quantum group associated with \mathscr A and R.