Ext-group in the category of quantum polynomial functors via the quantum Frobenius twist

TL;DR

This paper investigates how the quantum Frobenius twist influences Ext-groups in quantum polynomial functor categories, providing computational methods and formulas applicable in various characteristics, advancing understanding in quantum algebra.

Contribution

It introduces new formulas and computational techniques for Ext-groups affected by the quantum Frobenius twist, extending to arbitrary characteristic cases.

Findings

Derived formulas for Ext-groups via quantum Frobenius twist

Computed homologies of quantum de Rham and Koszul complexes

Progress toward a general Ext-group formula in arbitrary characteristic

Abstract

We study the effect of a quantum Frobenius twist on Ext-groups in the category of quantum polynomial functors. We use quantum versions of the de Rham and Koszul complexes, and compute their homologies. We use them to do several Ext-computations, and obtain a formula to compute Ext-groups between two functors obtained via the Frobenius, in characteristic zero or in big enough characteristic. Finally, we make some advancements toward a general formula in arbitrary characteristic.