Realization of PBW-deformations of type \(\mathbb{A}_n\) quantum groups via multiple Ore extensions. (English) Zbl 1439.17019

Xu, Yongjun; Huang, Hua-Lin; Wang, Dingguo

J. Pure Appl. Algebra 223, No. 4, 1531-1547 (2019).

Summary: The notion of multiple Ore extension

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is introduced as a natural generalization of Ore extensions and double Ore extensions. For a PBW-deformation \(\mathfrak{B}_q(\mathfrak{sl}(n + 1, \mathbb{C}))\) of type \(\mathbb{A}_n\) 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 \((1, 2, \cdots, n)\). Moreover, we analyze the quantum algebras \(\mathfrak{B}_q(\mathfrak{g})\) with \(\mathfrak{g}\) of type \(\mathbb{D}_4\), \(\mathbb{B}_2\) and \(\mathbb{G}_2\) and give some examples and counterexamples that can be realized by a ladder Ore extension.

© Elsevier B.V.

MSC:

17B37

Quantum groups (quantized enveloping algebras) and related deformations

Keywords:

multiple Ore extension; PBW-deformation; quantum groups

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