Quantum affine algebras at small root of unity

TL;DR

This paper investigates the structure of Frobenius-Lusztig kernels for quantum affine algebras at small roots of unity, revealing unexpected relations to larger affine Lie algebras and extending previous finite-dimensional Lie algebra results.

Contribution

It uncovers the structure of Frobenius-Lusztig kernels at small roots of unity, showing their connection to larger affine Lie algebras, which was previously unexplored.

Findings

Frobenius-Lusztig kernels are related to larger affine Lie algebras

Small root of unity cases are degenerate and special

Extends previous work on quantum groups for finite-dimensional Lie algebras

Abstract

We study the Frobenius-Lusztig kernel for quantum affine algebras at root of unity of small orders that are usually excluded in literature. These cases are somewhat degenerate and we find that the kernel is in fact mostly related to different affine Lie algebras, some even of larger rank, that exceptionally sit inside the quantum affine algebra. This continues the authors study for quantum groups associated to finite-dimensional Lie algebras in [Len14c].