Quantum Troesch complex

TL;DR

The paper investigates quantum Frobenius twists' impact on Ext-groups in quantum polynomial categories, introducing quantum Troesch complexes that facilitate spectral sequence construction for twisted functors.

Contribution

It introduces quantum Troesch complexes and demonstrates their role in computing Ext-groups of twisted functors at roots of unity.

Findings

Quantum Troesch complexes enable spectral sequence construction.

Constructed quantum Troesch complexes at roots of unity of order 3.

Established connections between quantum Frobenius twist and Ext-groups.

Abstract

We study the effect of quantum Frobenius twist on Ext-groups in the category of quantum polynomial, and prove that the existence of type of complexes, called quantum Troesch complexes, enables the construction of a spectral sequence computing the Ext groups of twisted functors from the knowledge of Ext-groups of the original functors. We then construct quantum Troesch complexes in the special case where the parameters of the quantum deformation is a root of unity of order 3.