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.

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Acknowledgements

This research is partially supported by Wang’s NSF Grant DMS-1702254 (including GRA supports for the two junior authors). WW thanks Adacemia Sinica Institute of Mathematics (Taipei) for the hospitality and support during a past visit, where some of the work was carried out.

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Correspondence to Weiqiang Wang.

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Chung, C., Sale, T. & Wang, W. Quantum supergroups VI: roots of 1. Lett Math Phys 109, 2753–2777 (2019). https://doi.org/10.1007/s11005-019-01209-4

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Keywords

  • Quantum groups
  • Quantum covering groups
  • Roots of 1
  • Frobenius–Lusztig homomorphism

Mathematics Subject Classification

  • Primary 17B37