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تسجيل مستخدم جديدLocalizations for quiver Hecke algebras
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We provide the localization procedure for monoidal categories by a real commuting family of braiders. For an element $w$ of the Weyl group, $mathscr{C}_w$ is a subcategory of modules over quiver Hecke algebra which categorifies the quantum unipotent coordinate algebra $A_q[mathfrak{n}(w)]$. We construct the localization $widetilde{mathscr{C}_w}$ of $mathscr{C}_w$ by adding the inverses of simple modules which correspond to the frozen variables in the quantum cluster algebra $A_q[mathfrak{n}(w)]$. The localization $widetilde{mathscr{C}_w}$ is left rigid and we expect that it is rigid.
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