Quantum symmetric pairs at roots of $1$

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 ıquantum group at roots of 1. We generalize Lusztig's quantum Frobenius morphism in this new setting. We define the small ıquantum group and compute its dimension.

Serre-Lusztig relations for $\imath$quantum groups

“…The Serre-Lusztig relations can be useful in the further study of ıquantum groups with q being a root of 1 (cf. [BS19]), which according to [BaV14,BaV15] may play a central role in the identification of the symmetries of the Hamiltonian of the XXZ open spin chain.…”