In a seminal paper, Drinfel’d explained how to associate with every classical r -matrix, which are called triangular r -matrices by some authors, for a Lie algebra $$ \mathfrak {g}$$ g a twisting element based on $${\mathcal {U}}(\mathfrak {g})[[\hbar ]]$$ U ( g ) [ [ ħ ] ] , or equivalently a left invariant star product quantizing the left-invariant Poisson structure corresponding to r on the 1-connected Lie group G of $$\mathfrak {g}$$ g . In a recent paper, the authors solve the same problem by means of Fedosov quantization. In this short note, we provide a connection between the two constructions by computing the characteristic (Fedosov) class of the twist constructed by Drinfel’d and proving that it is the trivial class given by $$ \frac{[\omega ]}{\hbar }$$ [ ω ] ħ .

中文翻译：

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由 Drinfel'd 构造的扭曲的特征 (Fedosov-) 类

在一篇开创性的论文中，Drinfel'd 解释了如何与每个经典的 r 矩阵相关联，一些作者称之为三角 r 矩阵，用于李代数 $$ \mathfrak {g}$$ ga 扭曲元素基于 $$ {\mathcal {U}}(\mathfrak {g})[[\hbar ]]$$ ​​U ( g ) [ [ ħ ] ] ，或等效地量化对应于 r 的左不变泊松结构的左不变星积$$\mathfrak {g}$$ g 的 1-连通李群 G 。在最近的一篇论文中，作者通过 Fedosov 量化解决了同样的问题。在这个简短的说明中，我们通过计算由 Drinfel'd 构造的扭曲的特征 (Fedosov) 类并证明它是由 $$ \frac{[\omega ]}{给出的平凡类来提供两种结构之间的联系\hbar }$$ [ ω ] ħ 。