The wonderful compactification for quantum groups Ganev, Iordan V ddc:510 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. Wiley 2019 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/5 https://research-explorer.ista.ac.at/download/5/7238 Ganev IV. The wonderful compactification for quantum groups. <i>Journal of the London Mathematical Society</i>. 2019;99(3):778-806. doi:<a href="https://doi.org/10.1112/jlms.12193">10.1112/jlms.12193</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1112/jlms.12193 info:eu-repo/semantics/altIdentifier/wos/000470025900008 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess