@article{5,
  abstract     = {In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix coefficients, and from its realization as a GIT quotient of the Vinberg semigroup. In order to define the wonderful compactification for a quantum group, we adopt a generalized formalism of Proj categories in the spirit of Artin and Zhang. Key to our construction is a quantum version of the Vinberg semigroup, which we define as a q-deformation of a certain Rees algebra, compatible with a standard Poisson structure. Furthermore, we discuss quantum analogues of the stratification of the wonderful compactification by orbits for a certain group action, and provide explicit computations in the case of SL2.},
  author       = {Ganev, Iordan V},
  journal      = {Journal of the London Mathematical Society},
  number       = {3},
  pages        = {778--806},
  publisher    = {Wiley},
  title        = {{The wonderful compactification for quantum groups}},
  doi          = {10.1112/jlms.12193},
  volume       = {99},
  year         = {2019},
}

@article{322,
  abstract     = {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.},
  author       = {Ganev, Iordan V},
  journal      = {Journal of Algebra},
  pages        = {92 -- 128},
  publisher    = {World Scientific Publishing},
  title        = {{Quantizations of multiplicative hypertoric varieties at a root of unity}},
  doi          = {10.1016/j.jalgebra.2018.03.015},
  volume       = {506},
  year         = {2018},
}