article published yes Iordan V Ganev author 447491B8-F248-11E8-B48F-1D18A9856A87 TaHa department 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. https://research-explorer.ista.ac.at/download/5/7238/2019_Wiley_Ganev.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Wiley2019 eng 00047002590000810.1112/jlms.12193 993778-806 Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” <i>Journal of the London Mathematical Society</i>. Wiley, 2019. <a href="https://doi.org/10.1112/jlms.12193">https://doi.org/10.1112/jlms.12193</a>. Ganev, Iordan V. “The Wonderful Compactification for Quantum Groups.” <i>Journal of the London Mathematical Society</i>, vol. 99, no. 3, Wiley, 2019, pp. 778–806, doi:<a href="https://doi.org/10.1112/jlms.12193">10.1112/jlms.12193</a>. Ganev, I. V. (2019). The wonderful compactification for quantum groups. <i>Journal of the London Mathematical Society</i>. Wiley. <a href="https://doi.org/10.1112/jlms.12193">https://doi.org/10.1112/jlms.12193</a> Ganev IV. 2019. The wonderful compactification for quantum groups. Journal of the London Mathematical Society. 99(3), 778–806. I.V. Ganev, Journal of the London Mathematical Society 99 (2019) 778–806. 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> I. V. Ganev, “The wonderful compactification for quantum groups,” <i>Journal of the London Mathematical Society</i>, vol. 99, no. 3. Wiley, pp. 778–806, 2019. 52018-12-11T11:44:06Z2023-09-19T10:13:08Z