On the universal Drinfeld–Yetter algebra

Abstract

The universal Drinfeld–Yetter algebra is an associative algebra whose co–Hochschild cohomology controls the existence of quantization functors of Lie bialgebras, such as the renowned one due to Etingof and Kazhdan. It was initially introduced by Enriquez, and later re-interpreted by Appel and Toledano Laredo as an algebra of endomorphisms in the colored PROP of a Drinfeld–Yetter module over a Lie bialgebra. Its vector space and algebra structure present a deep and mysterious connection with symmetric groups of all orders. In this paper, we provide an explicit formula for its structure constants in terms of certain combinatorial diagrams, which we term Drinfeld–Yetter looms.