{"doi":"10.1112/jlms.12193","month":"06","abstract":[{"lang":"eng","text":"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."}],"ddc":["510"],"isi":1,"has_accepted_license":"1","status":"public","oa_version":"Published Version","_id":"5","publication":"Journal of the London Mathematical Society","volume":99,"file":[{"content_type":"application/pdf","file_name":"2019_Wiley_Ganev.pdf","date_updated":"2020-07-14T12:46:35Z","creator":"kschuh","checksum":"1be56239b2cd740a0e9a084f773c22f6","file_id":"7238","date_created":"2020-01-07T13:31:53Z","file_size":431754,"relation":"main_file","access_level":"open_access"}],"issue":"3","citation":{"mla":"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>.","ieee":"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.","apa":"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>","ama":"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>","chicago":"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>.","ista":"Ganev IV. 2019. The wonderful compactification for quantum groups. Journal of the London Mathematical Society. 99(3), 778–806.","short":"I.V. Ganev, Journal of the London Mathematical Society 99 (2019) 778–806."},"day":"01","title":"The wonderful compactification for quantum groups","scopus_import":"1","intvolume":"        99","date_created":"2018-12-11T11:44:06Z","author":[{"first_name":"Iordan V","id":"447491B8-F248-11E8-B48F-1D18A9856A87","full_name":"Ganev, Iordan V","last_name":"Ganev"}],"article_processing_charge":"Yes (via OA deal)","page":"778-806","type":"journal_article","publisher":"Wiley","date_updated":"2023-09-19T10:13:08Z","publication_status":"published","department":[{"_id":"TaHa"}],"year":"2019","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"date_published":"2019-06-01T00:00:00Z","file_date_updated":"2020-07-14T12:46:35Z","publist_id":"8052","external_id":{"isi":["000470025900008"]},"language":[{"iso":"eng"}],"quality_controlled":"1","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"}