10.1016/j.jalgebra.2018.03.015
Ganev, Iordan V
Iordan V
Ganev
Quantizations of multiplicative hypertoric varieties at a root of unity
World Scientific Publishing
2018
2018-12-11T11:45:49Z
2020-01-16T12:36:52Z
journal_article
https://research-explorer.app.ist.ac.at/record/322
https://research-explorer.app.ist.ac.at/record/322.json
1412.7211
We construct quantizations of multiplicative hypertoric varieties using an algebra of q-difference operators on affine space, where q is a root of unity in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the multiplicative hypertoric variety and admits an explicit finite étale splitting. The global sections of this Azumaya algebra is a hypertoric quantum group, and we prove a localization theorem. We introduce a general framework of Frobenius quantum moment maps and their Hamiltonian reductions; our results shed light on an instance of this framework.