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Biquantization of the necklace Lie bialgebra

Xiaojun ChenSchool of Mathematics , Sichuan University , Chengdu , Sichuan Province , 610064 P.R. ChinaMaozhou HuangDepartment of Mathematics , New Uzbekistan University , Tashkent , 100001 UzbekistanMeiliang LiuNational University of UzbekistanJun ZhangNational University of Uzbekistan

2026

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Annotatsiya

For the double of a quiver, the works of Ginzburg, Bocklandt-Le Bruyn and Schedler show that its closed paths, called the necklaces, have a natural Lie bialgebra structure. Schedler also constructed,in [Int. Math. Res. Notices, 2005 (12), 725-760], a Hopf algebra that quantizes this Lie bialgebra. In this paper, we pursue one more step in this direction by constructing its biquantization, in the sense of Turaev [Ann. Sci. École Norm. Sup. (4) 24 (1991), no. 6, 635-704].

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DOI: 10.48550/arxiv.2604.02853

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