论文标题
ding-iohara量子代数的动态类似物
A dynamical analogue of Ding-Iohara quantum algebras
论文作者
论文摘要
我们介绍了一个动态HOPF代数$ u_ {q，p}（g，x_l）$的家族，具体取决于复杂的参数$ q $，正式参数$ p $，一个$ g $的结构函数，满足所谓的ding-iohara条件，以及类型$ x_l $的有限根系。如果$ g $设置为某些theta函数，则我们的家人恢复椭圆形代数$ u_ {q，p}（\ widehat {\ sathfrak {\ mathfrak {g}}）$ for Untwisted offine lie代数lie代数$ \ wideHat {\ mathfrak {\ mathfrak { Jimbo-Konno-odake-Shiraishi（1999）和Farghly-Konno-Ishima（2014）。另外，在情况下采取限制$ p \ to 0 $，$ x_l = a_l $，我们恢复了带有结构函数$ a_l $的type $ a_l $的Hopf代数$ u_q（\ overline {g}，a_l）$ a_L $ \ overline unline functions $ \ overline {g}仿射代数。因此，我们的Hopf代数$ u_ {q，p}（g，x_l）$可以被视为ding-iohara量子代数的动态类似物。作为副产品，我们获得了ding-iohara量子代数的扩展，向非较小型类型的代数延伸。
We introduce a family of dynamical Hopf algebroids $U_{q,p}(g,X_l)$ depending on a complex parameter $q$, a formal parameter $p$, a set $g$ of structure functions satisfying the so-called Ding-Iohara condition, and a finite root system of type $X_l$. If $g$ is set to be certain theta functions, then our family recovers the elliptic algebras $U_{q,p}(\widehat{\mathfrak{g}})$ for untwisted affine Lie algebras $\widehat{\mathfrak{g}}$ studied by Konno (1998, 2009), Jimbo-Konno-Odake-Shiraishi (1999) and Farghly-Konno-Oshima (2014). Also, taking the limit $p \to 0$ in the case $X_l=A_l$, we recover the Hopf algebras $U_q(\overline{g},A_l)$ of type $A_l$ with structure functions $\overline{g} := \lim_{p \to 0} g$, introduced by Ding-Iohara (1998) as a generalization of Drinfeld quantum affine algebras. Thus, our Hopf algebroid $U_{q,p}(g,X_l)$ can be regarded as a dynamical analogue of the Ding-Iohara quantum algebras. As a byproduct, we obtain an extension of the Ding-Iohara quantum algebras to those of non-simply-laced type.
