[{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","type":"journal_article","page":"778-806","doi":"10.1112/jlms.12193","oa_version":"Published Version","publication":"Journal of the London Mathematical Society","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"isi":1,"intvolume":"        99","oa":1,"publisher":"Wiley","quality_controlled":"1","status":"public","date_published":"2019-06-01T00:00:00Z","abstract":[{"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.","lang":"eng"}],"ddc":["510"],"file":[{"creator":"kschuh","checksum":"1be56239b2cd740a0e9a084f773c22f6","date_created":"2020-01-07T13:31:53Z","relation":"main_file","file_name":"2019_Wiley_Ganev.pdf","date_updated":"2020-07-14T12:46:35Z","access_level":"open_access","file_size":431754,"file_id":"7238","content_type":"application/pdf"}],"author":[{"first_name":"Iordan V","id":"447491B8-F248-11E8-B48F-1D18A9856A87","last_name":"Ganev","full_name":"Ganev, Iordan V"}],"month":"06","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","file_date_updated":"2020-07-14T12:46:35Z","_id":"5","date_updated":"2023-09-19T10:13:08Z","citation":{"short":"I.V. Ganev, Journal of the London Mathematical Society 99 (2019) 778–806.","ista":"Ganev IV. 2019. The wonderful compactification for quantum groups. Journal of the London Mathematical Society. 99(3), 778–806.","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>","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>.","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>","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."},"department":[{"_id":"TaHa"}],"publication_status":"published","date_created":"2018-12-11T11:44:06Z","day":"01","title":"The wonderful compactification for quantum groups","external_id":{"isi":["000470025900008"]},"publist_id":"8052","volume":99,"issue":"3","year":"2019"},{"_id":"322","date_updated":"2023-09-15T12:08:38Z","project":[{"_id":"25E549F4-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Arithmetic and physics of Higgs moduli spaces","grant_number":"320593"}],"citation":{"ieee":"I. V. Ganev, “Quantizations of multiplicative hypertoric varieties at a root of unity,” <i>Journal of Algebra</i>, vol. 506. World Scientific Publishing, pp. 92–128, 2018.","chicago":"Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” <i>Journal of Algebra</i>. World Scientific Publishing, 2018. <a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">https://doi.org/10.1016/j.jalgebra.2018.03.015</a>.","ama":"Ganev IV. Quantizations of multiplicative hypertoric varieties at a root of unity. <i>Journal of Algebra</i>. 2018;506:92-128. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">10.1016/j.jalgebra.2018.03.015</a>","mla":"Ganev, Iordan V. “Quantizations of Multiplicative Hypertoric Varieties at a Root of Unity.” <i>Journal of Algebra</i>, vol. 506, World Scientific Publishing, 2018, pp. 92–128, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">10.1016/j.jalgebra.2018.03.015</a>.","short":"I.V. Ganev, Journal of Algebra 506 (2018) 92–128.","apa":"Ganev, I. V. (2018). Quantizations of multiplicative hypertoric varieties at a root of unity. <i>Journal of Algebra</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1016/j.jalgebra.2018.03.015\">https://doi.org/10.1016/j.jalgebra.2018.03.015</a>","ista":"Ganev IV. 2018. Quantizations of multiplicative hypertoric varieties at a root of unity. Journal of Algebra. 506, 92–128."},"department":[{"_id":"TaHa"}],"publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1412.7211","open_access":"1"}],"date_created":"2018-12-11T11:45:49Z","external_id":{"isi":["000433270600005"],"arxiv":["1412.7211"]},"day":"15","title":"Quantizations of multiplicative hypertoric varieties at a root of unity","volume":506,"acknowledgement":"National Science Foundation: Graduate Research Fellowship and grant No.0932078000; ERC Advanced Grant “Arithmetic and Physics of Higgs moduli spaces” No. 320593 \r\nThe author is grateful to David Jordan for suggesting this project and providing guidance throughout, particularly for the formulation of Frobenius quantum moment maps and key ideas in the proofs of Theorems 3.12 and 4.8. Special thanks to David Ben-Zvi (the author's PhD advisor) for numerous discussions and constant encouragement, and for suggesting the term ‘hypertoric quantum group.’ Many results appearing in the current paper were proven independently by Nicholas Cooney; the author is grateful to Nicholas for sharing his insight on various topics, including Proposition 3.8. The author also thanks Nicholas Proudfoot for relating the definition of multiplicative hypertoric varieties, as well as the content of Remark 2.14. The author also benefited immensely from the close reading and detailed comments of an anonymous referee, and from conversations with Justin Hilburn, Kobi Kremnitzer, Michael McBreen, Tom Nevins, Travis Schedler, and Ben Webster. \r\n\r\n\r\n\r\n","publist_id":"7543","year":"2018","doi":"10.1016/j.jalgebra.2018.03.015","page":"92 - 128","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","type":"journal_article","publication":"Journal of Algebra","oa_version":"Preprint","arxiv":1,"ec_funded":1,"language":[{"iso":"eng"}],"oa":1,"publisher":"World Scientific Publishing","isi":1,"intvolume":"       506","status":"public","quality_controlled":"1","date_published":"2018-07-15T00:00:00Z","abstract":[{"text":"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.","lang":"eng"}],"scopus_import":"1","article_processing_charge":"No","author":[{"first_name":"Iordan V","id":"447491B8-F248-11E8-B48F-1D18A9856A87","last_name":"Ganev","full_name":"Ganev, Iordan V"}],"month":"07"}]