8 citations · 21 across the 39 of their papers we have counts for
41 papers
Representation-tame Geiß-Leclerc-Schröer algebras and a revised GLS conjecture on root systems
Qiang Dong, Zengqiang Lin, Ming Lu +1
Using Galois covering theory and equivariant techniques, we classify all connected representation-tame Geiß--Leclerc--Schröer (GLS) algebras in terms of their defining triples $(C,…
Quantum supersymmetric pairs and the Serre relations via Hopf algebras
Jiayi Chen, Shiquan Ruan, Hongying Zhu
We study iHopf algebras associated with quantum supergroups of basic type. For a quantum supersymmetric pair , we realize and $…
Twisted quantum loop algebras via semi-derived Ringel-Hall algebras
Ming Lu, Shiquan Ruan
Twisted quantum loop algebras are a generalization of twisted quantum affine algebras in Drinfeld new presentation. The Hall algebras of Geigle--Lenzing's weighted projective lines…
Frobenius quotients, inflation categories and weighted projective lines
Xiao-Wu Chen, Qiang Dong, Shiquan Ruan
We propose the notion of Frobenius quotients between Frobenius exact categories. It turns out that any Frobenius quotient induces Frobenius quotients between the corresponding infl…
Double Hall-Littlewood symmetric polynomials
Jiayi Chen, Ming Lu, Shiquan Ruan
We establish a ring isomorphism between the derived Hall algebra of the Jordan quiver and the ring of double symmetric functions (i.e., the ring of symmetric polynomials in two set…
iQuantum groups and iHopf algebras II: dual canonical bases
Jiayi Chen, Ming Lu, Xiaolong Pan +2
Building on the iHopf algebra realization of quasi-split universal iquantum groups developed in a prequel, we construct the dual canonical basis for a universal iquantum group of a…
iQuantum groups and iHopf algebras I: foundation
Jiayi Chen, Ming Lu, Xiaolong Pan +2
We introduce the notion of iHopf algebra, a new associative algebra structure defined on a Hopf algebra equipped with a Hopf pairing. The iHopf algebra on a Borel quantum group end…
ACM tilting bundles on a Geigle-Lenzing projective plane of type
Jianmin Chen, Shiquan Ruan, Weikang Weng
Let be a Geigle-Lenzing projective plane of type and the category of coherent sheaves on . This paper is devoted to s…
Hopf algebras associated with self-dual Hopf algebras
Jiayi Chen, Shiquan Ruan
Motivated by the construction of Hall algebras and -Hall algebras, we introduce Hopf algebras associated with symmetrically self-dual Hopf algebras. We prove tha…
Hall Polynomials for Weighted projective lines
Jiayi Chen, Bangming Deng, Shiquan Ruan
This paper deals with the triangle singularity defined by the \linebreak equation for weight triple , as well as the category of co…
Analogue of Feigin's map on quantum group of split type
Ming Lu, Shiquan Ruan, Haicheng Zhang
The (universal) quantum groups are as a vast generalization of (Drinfeld double) quantum groups. We establish an algebra homomorphism from universal quantum group o…
Brieskorn-Pham singularities via ACM bundles on Geigle-Lenzing projective spaces
Jianmin Chen, Shiquan Ruan, Weikang Weng
We study the singularity category of the Brieskorn-Pham singularity , associated with the Geigle-Lenzing projective space $\mathbb{…
Hall algebras of weighted projective lines and quantum symmetric pairs III: quasi-split type
Ming Lu, Shiquan Ruan
From a category with an involution , we introduce -complexes, which are a generalization of (bounded) complexes, periodic complexes and modules of $…
Geometric model for vector bundles via infinite marked strips
Jianmin Chen, Shiquan Ruan, Jinfeng Zhang
We present a geometric model for the category of vector bundles over the weighted projective line of type (2,2,n). This model is based on the orbit space of an infinite marked stri…
Hall algebras of weighted projective lines and quantum symmetric pairs II: injectivity
Ming Lu, Shiquan Ruan
We show that the morphism from the quantum loop algebra of split type to the Hall algebra of the weighted…
On two open questions for extension bundles
Qiang Dong, Shiquan Ruan
In this paper we give positive answers for two open questions on extension bundles over weighted projective lines, raised by Kussin, Lenzing and Meltzer in the paper ``Triangle sin…
Geometric model for weighted projective lines of type
Jianmin Chen, Shiquan Ruan, Hongxia Zhang
We give a geometric model for the category of coherent sheaves over the weighted projective line of type in terms of an annulus with marked points on its boundary. We estab…
Quantum Borcherds-Bozec algebras via semi-derived Ringel-Hall algebras II: braid group actions
Ji Lin, Ming Lu, Shiquan Ruan
Based on the realization of quantum Borcherds-Bozec algebra and quantum generalized Kac-Moody algebra via semi-derived Ringel-…
Stability approach to torsion pairs on abelian categories
Mingfa Chen, Yanan Lin, Shiquan Ruan
In this paper we introduce a local-refinement procedure to investigate stability data on an abelian category, and provide a sufficient and necessary condition for a stability data…
Derived Hall algebras of root categories
Jiayi Chen, Ming Lu, Shiquan Ruan
For a finitary hereditary abelian category , we define a derived Hall algebra of its root category by counting the triangles and using the octahedral axiom, which is p…
New realization of quantum groups via -Hall algebras
Jiayi Chen, Yanan Lin, Shiquan Ruan
For an essentially small hereditary abelian category , we define a new kind of algebra , called the -Hall algebra of . The…
Derived equivalences between one-branch extensions of "rectangles"
Qiang Dong, Yanan Lin, Shiquan Ruan
In this paper we investigate the incidence algebras arising from one-branch extensions of "rectangles". There are four different ways to form such extensions, and all four kinds of…
Nakayama algebras and Fuchsian singularities
Helmut Lenzing, Hagen Meltzer, Shiquan Ruan
This present paper is devoted to the study of a class of Nakayama algebras given by the path algebra of the equioriented quiver subject to the nilpotency de…
quantum groups of split type via derived Hall algebras
Jiayi Chen, Ming Lu, Shiquan Ruan
A quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an quantum group) with parameters…