Biquantization of the necklace Lie bialgebra
Xiaojun Chen, Maozhou Huang, Meiliang Liu, and Jun Zhang
TL;DR
This paper constructs a biquantization of the Lie bialgebra structure on necklaces of a quiver's double, extending previous quantization work by Turaev.
Contribution
It introduces a novel biquantization framework for the necklace Lie bialgebra, advancing the understanding of its algebraic and geometric properties.
Findings
Constructed a biquantization of the necklace Lie bialgebra.
Extended Turaev's biquantization framework to this setting.
Provides new tools for studying quiver-related algebraic structures.
Abstract
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. \'Ecole Norm. Sup. (4) 24 (1991), no. 6, 635-704].
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