Quantum multiplicative hypertoric varieties and localization

Thesis

In this thesis, we consider q-deformations of multiplicative Hypertoric varieties, where q∈𝕂^x for 𝕂 an algebraically closed field of characteristic 0. We construct an algebra 𝒟_q of q-difference operators as a Heisenberg double in a braided monoidal category. We then focus on the case where q is specialized to a root of unity. In this setting, we use 𝒟_q to construct an Azumaya algebra on an l-twist of the multiplicative Hypertoric variety, before showing that this algebra splits over the fibers of both the moment and resolution maps. Finally, we sketch a derived localization theorem for these Azumaya algebras.

Authors: Cooney, N

• Publication date: 2014
• DOI: 10.5287/ora-wvab1znkk
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Braided Tensor Categories; Quantum Algebra; Azumaya algebras; Representation Theory
• Subjects: Algebraic geometry; Mathematics; Group theory and generalizations (mathematics)