论文标题
扬吉人的限制量子双重
The restricted quantum double of the Yangian
论文作者
论文摘要
令$ \ mathfrak {g} $为一个复杂的半imple lie代数，与关联的yangian $ y_ \ hbar \ hbar \ mathfrak {g} $。 In the mid-1990s, Khoroshkin and Tolstoy formulated a conjecture which asserts that the algebra $\mathrm{D}Y_\hbar\mathfrak{g}$ obtained by doubling the generators of $Y_\hbar\mathfrak{g}$, called the Yangian double, provides a realization of the quantum double of the Yangian.我们在$ \ mathbb {c} [\！[\ hbar] \！] $上提供了统一的猜想证明，该证明与量化包络代数的理论兼容。作为副产品，我们确定了扬anian的通用$ r $ r $ -matrix，其规范元素由扬吉亚人与其受限制的二元组合所定义。
Let $\mathfrak{g}$ be a complex semisimple Lie algebra with associated Yangian $Y_\hbar\mathfrak{g}$. In the mid-1990s, Khoroshkin and Tolstoy formulated a conjecture which asserts that the algebra $\mathrm{D}Y_\hbar\mathfrak{g}$ obtained by doubling the generators of $Y_\hbar\mathfrak{g}$, called the Yangian double, provides a realization of the quantum double of the Yangian. We provide a uniform proof of this conjecture over $\mathbb{C}[\![\hbar]\!]$ which is compatible with the theory of quantized enveloping algebras. As a byproduct, we identify the universal $R$-matrix of the Yangian with the canonical element defined by the pairing between the Yangian and its restricted dual.
