$ı$quantum groups of split type via derived Hall algebras

Abstract

A quantum symmetric pair consists of a quantum group $\mathbf{U}$ and its coideal subalgebra ${\mathbf{U}}_{\ddot{\mathbf{I}}‚}^{ı}$ (called an $ı$quantum group) with parameters $\ddot{\mathbf{I}}‚$. In this note, we use the derived Hall algebras of 1-periodic complexes to realize the $ı$quantum groups ${\mathbf{U}}_{\ddot{\mathbf{I}}‚}^{ı}$ of split type.

14 pages, minor edits, accepted by Journal of Algebra. arXiv admin note: text overlap with arXiv:2110.02575