We introduce a family of dynamical Hopf algebroids depending on a complex parameter q, a formal parameter p, a set of structure functions satisfying the so-called Ding-Iohara condition, and a finite root system. If the set of function is set to be certain theta functions, then our family recovers the elliptic algebras for untwisted affine Lie algebras introduced by Jimbo, Konno, Odake and Shiraishi(1999). Also, taking p → 0 for in the case the root system of type A_l, we recover the Hopf algebras of type A_l introduced by Ding and Iohara as a generalization of Drinfeld quantum affine algebras. Thus, our Hopf algebroid 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. This talk is based on the joint work with Shintaro Yanagida (arXiv:2210.02777).

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