量子环代数上的一个新余积
A new new coproduct on quantum loop algebras
AI总结：
本文在一般量子环代数上定义了一个余积，推广了Drinfeld-Jimbo余积，并用于证明R-矩阵的有理性、q-特征的乘性及theta级数的多项式性质。
摘要：
量子环代数推广了简单李代数$\mathfrak{g}$的$U_q(\widehat{\mathfrak{g}})$，并包括Kac-Moody李代数的量子仿射化、箭图的K-理论Hall代数以及环面Calabi-Yau三维流形的BPS代数等例子。在本文中，我们在一般量子环代数上定义了一个余积，该余积在$U_q(\widehat{\mathfrak{g}})$的特殊情形下与Drinfeld-Jimbo余积一致。我们利用这一构造证明了关于量子环代数表示的基本事实，例如$R$-矩阵的有理性、$q$-特征的乘性以及theta级数的多项式性质。
英文摘要：
Quantum loop algebras generalize $U_q(\widehat{\mathfrak{g}})$ for simple Lie algebras $\mathfrak{g}$, and they include examples such as quantum affinizations of Kac-Moody Lie algebras, K-theoretic Hall algebras of quivers, and BPS algebras for toric Calabi-Yau threefolds. In the present paper, we define a coproduct on general quantum loop algebras, which coincides with the Drinfeld-Jimbo coproduct in the particular case of $U_q(\widehat{\mathfrak{g}})$. We use our construction to prove fundamental facts about representations of quantum loop algebras, such as the rationality of $R$-matrices, multiplicativity of $q$-characters, and polynomiality of theta series.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
