Quantum supergroups VI. Roots of $1$

Abstract

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.

v2, 21 pages, mild corrections, Lett. Math. Phys. (to appear)