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arXiv · 1812.05771

Quantum supergroups VI. Roots of $1$

Christopher Chung·Thomas Sale·Weiqiang Wang
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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.

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BibTeXRIS

Christopher Chung, Thomas Sale, Weiqiang Wang. 2018-12-14. Quantum supergroups VI. Roots of $1$. https://doi.org/10.1007/s11005-019-01209-4

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