Localizations for quiver Hecke algebras
- 주제(키워드) Categorification , localization , monoidal category , quantum unipotent coordinate ring , quiver Hecke algebra
- 주제(기타) Mathematics, Applied
- 주제(기타) Mathematics
- 설명문(일반) [Kashiwara, Masaki] Kyoto Univ, Res Inst Math Sci, Inst Adv Study, Kyoto 6068502, Japan; [Kashiwara, Masaki] Korea Inst Adv Study, Seoul 02455, South Korea; [Kim, Myungho] Kyung Hee Univ, Dept Math, Seoul 02447, South Korea; [Oh, Se-Jin] Ewha Womans Univ, Dept Math, Seoul 120750, South Korea; [Park, Euiyong] Univ Seoul, Dept Math, Seoul 02504, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 INT PRESS BOSTON, INC
- 발행년도 2021
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000190359
- 본문언어 영어
초록/요약
In this paper, we provide a generalization of the localization procedure for monoidal categories developed in [12] by Kang-Kashiwara-Kim by introducing the notions of braiders and a real commuting family of braiders. Let R be a quiver Hecke algebra of arbitrary symmetrizable type and R-gmod the category of finite-dimensional graded R-modules. For an element w of the Weyl group, C-w is the subcategory of R-gmod which categorifies the quantum unipotent coordinate algebra A(q)(n(w)). We construct the localization (C) over tilde (w) of C-w by adding the inverses of simple modules M(w Lambda(i), Lambda(i)) which correspond to the frozen variables in the quantum cluster algebra A(q)(n(w)). The localization (C) over tilde (w) is left rigid and it is conjectured that (C) over tilde (w) is rigid.
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