Quantum supergroups VI: roots of 1

A quantum covering group is an algebra with parameters q and \(\pi \) subject to \(\pi ^2=1\), and it admits an integral form; it specializes to the usual quantum group at \(\pi =1\) and to a quantum supergroup of anisotropic type at \(\pi =-1\). In this paper we establish the Frobenius–Lusztig homomorphism and Lusztig–Steinberg tensor product theorem in the setting of quantum covering groups at roots of 1. The specialization of these constructions at \(\pi =1\) recovers Lusztig’s constructions for quantum groups at roots of 1.