2016/02/02 by Nicholas Cooney, Cooney, Nicholas
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.AG #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.1602.01045
31 pages. An edited version of the author's doctoral thesis. Any comments and corrections welcome
arxiv created 2016/02/02 · openalex publication_date 2016/02/02 · arxiv updated 2016/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider q-deformations of multiplicative hypertoric varieties, for q a non-zero element of an algebraically closed field of characteristic 0. We construct an algebra Dq 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 Dq 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.