Quantum tilting modules over local rings

Fiebig P (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal of the London Mathematical Society-Second Series London Mathematical Society

DOI: 10.1112/jlms.12714

Abstract

We show that tilting modules for quantum groups over local Noetherian domains of quantum characteristic 0 exist and the indecomposable tilting modules are parametrized by their highest weight. For this, we introduce a model category (Formula presented.) associated with a Noetherian (Formula presented.) -domain (Formula presented.) and a root system (Formula presented.). We show that if (Formula presented.) is of quantum characteristic (Formula presented.), the model category contains all (Formula presented.) -modules that admit a Weyl filtration. If (Formula presented.) is in addition local, we study torsion phenomena in the model category. This leads to a construction of torsion free, or “maximal” objects in (Formula presented.). We show that these correspond to tilting modules for the quantum group associated with (Formula presented.) and (Formula presented.).

Authors with CRIS profile

Peter Fiebig Professur für Mathematik (Algebra und Geometrie)

How to cite

APA:

Fiebig, P. (2023). Quantum tilting modules over local rings. Journal of the London Mathematical Society-Second Series. https://dx.doi.org/10.1112/jlms.12714

MLA:

Fiebig, Peter. "Quantum tilting modules over local rings." Journal of the London Mathematical Society-Second Series (2023).

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