Quantum symmetric pairs at roots of $1$

TL;DR

This paper explores the structure of quantum symmetric pairs at roots of unity, generalizing Lusztig's quantum Frobenius morphism and defining the small iquantum group with computed dimension.

Contribution

It introduces the iquantum group at roots of unity and extends the quantum Frobenius morphism to this setting, advancing the theory of quantum symmetric pairs.

Findings

Generalized Lusztig's quantum Frobenius morphism at roots of 1

Defined the small iquantum group and computed its dimension

Extended quantum group theory to symmetric pairs at roots of unity

Abstract

A quantum symmetric pair is a quantization of the symmetric pair of universal enveloping algebras. Recent development suggests that most of the theory for quantum groups can be generalised to the setting of quantum symmetric pairs. In this paper, we study the $\imath$quantum group at roots of $1$. We generalize Lusztig's quantum Frobenius morphism in this new setting. We define the small $\imath$quantum group and compute its dimension.