Realization of PBW-deformations of type An quantum groups via multiple Ore extensions

The notion of multiple Ore extension is introduced as a natural generalization of Ore extensions and double Ore extensions. For a PBW-deformation B-q(sl(n + 1, C)) of type A(n) quantum group, we explicitly obtain the commutation relations of its root vectors, then show that it can be realized via a series of multiple Ore extensions, which we call a ladder Ore extension of type (1, 2, ..., n). Moreover, we analyze the quantum algebras B-q(g) with g of type D-4, B-2 and G(2) and give some examples and counterexamples that can be realized by a ladder Ore extension. (C) 2018 Elsevier B.V. All rights reserved.