Formality theorem for Lie bialgebras and quantization of coboundary r-matrices
Formality theorem for Lie bialgebras and quantization of coboundary r-matrices
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发表时间：
2005-06
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通讯作者：
G. Halbout
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作者：
G. Halbout
设$（g，\delta_\hbar）$是一个李双代数。设$（U_\hbar（g），\Delta_\hbar）$是$（g，\delta_\hbar）$通过Etingof-Kazhdan函子的量子化。证明了李代数C（\g）=\Lambda（g）$与张量代数TU=T（U\hbar（g）[-1]）$之间存在一个L\infty$-态射.当$（g，\delta_\hbar，r）$是共边界李双代数时，我们从形式态射推导出$r$的量化$R $的存在性。
Let $(g,\delta_\hbar)$ be a Lie bialgebra. Let $(U_\hbar(g),\Delta_\hbar)$ a quantization of $(g,\delta_\hbar)$ through Etingof-Kazhdan functor. We prove the existence of a $L_\infty$-morphism between the Lie algebra $C(\g)=\Lambda(g)$ and the tensor algebra $TU=T(U_\hbar(g)[-1])$ with Lie algebra structure given by the Gerstenhaber bracket. When $(g,\delta_\hbar,r)$ is a coboundary Lie bialgebra, we deduce from the formality morphism the existence of a quantization $R$ of $r$.