# Hall algebras and quantum symmetric pairs of Kac-Moody type

@inproceedings{Lu2020HallAA, title={Hall algebras and quantum symmetric pairs of Kac-Moody type}, author={Ming Lu and Weiqiang Wang}, year={2020} }

We extend our ıHall algebra construction from acyclic to arbitrary ıquivers, where the ıquiver algebras are infinite-dimensional 1-Gorenstein in general. Then we establish an injective homomorphism from the universal ıquantum group of Kac-Moody type arising from quantum symmetric pairs to the ıHall algebra associated to a virtually acyclic ıquiver.

## 13 Citations

A Drinfeld type presentation of affine $\imath$quantum groups I: split ADE type

- Mathematics
- 2020

We establish a Drinfeld type new presentation for the $\imath$quantum groups arising from quantum symmetric pairs of split affine ADE type, which includes the $q$-Onsager algebra as the rank 1 case.…

Quantum symmetric pairs

- Mathematics
- 2021

This is a survey of some recent progress on quantum symmetric pairs and applications. The topics include quasi K-matrices, ıSchur duality, canonical bases, super Kazhdan-Lusztig theory, ıHall…

Differential operator approach to $\imath$quantum groups

- Mathematics
- 2022

For a quasi-split Satake diagram, we define a modified q-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding ıquantum group. In other words, we provide a…

ıquantum groups of split type via derived Hall algebras

- Mathematics, PhysicsJournal of Algebra
- 2022

Hall algebras and quantum symmetric pairs I: Foundations

- MathematicsProceedings of the London Mathematical Society
- 2022

A quantum symmetric pair consists of a quantum group U$\mathbf {U}$ and its coideal subalgebra Uςı${\mathbf {U}}^{\imath }_{\bm{\varsigma }}$ with parameters ς$\bm{\varsigma }$ (called an ı$\imath$…

Pseudo-symmetric pairs for Kac-Moody algebras

- Mathematics
- 2021

Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are well-studied in the context of symmetrizable KacMoody algebras.…

Braid group symmetries on quasi-split $\imath$quantum groups via $\imath$Hall algebras

- Mathematics
- 2021

We establish automorphisms with closed formulas on quasi-split ıquantum groups of symmetric Kac-Moody type associated to restricted Weyl groups. The proofs are carried out in the framework of ıHall…

BRAID GROUP SYMMETRIES ON QUASI-SPLIT ıQUANTUM GROUPS VIA ıHALL ALGEBRAS

- Mathematics
- 2021

We establish automorphisms with closed formulas on quasi-split ıquantum groups of symmetric Kac-Moody type associated to restricted Weyl groups. The proofs are carried out in the framework of ıHall…

$\imath$Hall algebra of Jordan quiver and $\imath$Hall-Littlewood functions

- Mathematics
- 2021

We show that the ıHall algebra of the Jordan quiver is a polynomial ring in infinitely many generators and obtain transition relations among several generating sets. We establish a ring isomorphism…

A Drinfeld type presentation of affine $\imath$quantum groups II: split BCFG type

- Mathematics
- 2021

Recently, Lu and Wang formulated a Drinfeld type presentation for ıquantum group Ũı arising from quantum symmetric pairs of split affine ADE type. In this paper, we generalize their results by…

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