Biquantization of the necklace Lie bialgebra
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910099995361280 |
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| author | Chen, Xiaojun Huang, Maozhou Liu, Meiliang Zhang, Jun |
| author_facet | Chen, Xiaojun Huang, Maozhou Liu, Meiliang Zhang, Jun |
| contents | 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]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_02853 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Biquantization of the necklace Lie bialgebra Chen, Xiaojun Huang, Maozhou Liu, Meiliang Zhang, Jun Rings and Algebras 16S38, 16T05 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]. |
| title | Biquantization of the necklace Lie bialgebra |
| topic | Rings and Algebras 16S38, 16T05 |
| url | https://arxiv.org/abs/2604.02853 |