Huanhuan Li

activity

20152026

most citedGraded Steinberg algebras and their representations

47 citations · 85 across the 24 of their papers we have counts for

collaborators

24 papers

math.RA2026

Some more talents of the talented monoid of a higher-rank graph

Roozbeh Hazrat, Huanhuan Li, Promit Mukherjee

In this paper, we explore the idea that the graded Grothendieck group $K_{0}^{g r}$ , or equivalently its positive cone, the talented monoid, can detect the structural type of higher-r…

math.RA2022★ 1 cited

How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings

Yajun Ma, Jiafeng Lü, Huanhuan Li +1

Let $Δ = (A_{B} M_{A}_{A} N_{B} B)$ be a Morita ring with $M \otimes_{A} N = 0 = N \otimes_{B} M$ .We first study how to construct (comple…

math.KT2020

The singularity category of an exact category applied to characterize Gorenstein schemes

Lars Winther Christensen, Nanqing Ding, Sergio Estrada +3

We study singularity categories of exact categories with a focus on those associated to a complete hereditary cotorsion pair. As an application we identify a non-affine analogue of…

math.RT2020

2-recollements of singualrity categories and Gorenstein defect categories over triangular matrix algebras

Huanhuan Li, Dandan Yang, Yuefei Zheng +1

Let $T = (A, M, 0, B)$ be a triangular matrix algebra with its corner algebras $A$ and $B$ Artinian and $_{A} M_{B}$ an $A$ - $B$ -bimodule. The 2-recollement structures for singularity categor…

math.RA2020★ 2 cited

Frobenius functors and Gorenstein projective precovers

Jiangsheng Hu, Huanhuan Li, Jiafeng Lu +1

We establish relations between Gorenstein projective precovers linked by Frobenius functors. This is motivated by an open problem that how to find general classes of rings for whic…

math.RT2020★ 4 cited

Leavitt path algebras, $B_{\infty}$ -algebras and Keller's conjecture for singular Hochschild cohomology

Xiao-Wu Chen, Huanhuan Li, Zhengfang Wang

For a finite quiver without sinks, we establish an isomorphism in the homotopy category $Ho (B_{\infty})$ of $B_{\infty}$ -algebras between the Hochschild cochain complex of…

math.RA2020★ 5 cited

When the Schur functor induces a triangle-equivalence between Gorenstein defect categories

Huanhuan Li, Jiangsheng Hu, Yuefei Zheng

Let $R$ be an Artin algebra and $e$ an idempotent of $R$ . Assume that $Tor_{i}^{e R e} (R e, G) = 0$ for any $G \in GProj e R e$ and $i$ sufficiently large. Necessary and sufficient…

math.RA2019★ 2 cited

A note on the core of Steinberg algebras

Roozbeh Hazrat, Huanhuan Li

For an ample Hausdorff groupoid $G$ , and the Steinberg algebra $A_{R} (G)$ with coefficients in the commutative ring $R$ with unit, we describe the centraliser of subalgebra $A_{R} (U)$ …

math.RA2019

Gorenstein projective modules and recollements over triangular matrix rings

Huanhuan Li, Yuefei Zheng, Jiangsheng Hu +1

Let $T = (R M 0 S)$ be a triangular matrix ring with $R$ and $S$ rings and $_{R} M_{S}$ an $R$ - $S$ -bimodule. We describe Gorenstein project…

math.RA2019★ 1 cited

Graded $K$ -Theory, Filtered $K$ -theory and the classification of graph algebras

Pere Ara, Roozbeh Hazrat, Huanhuan Li

We prove that an isomorphism of graded Grothendieck groups $K_{0}^{g r}$ of two Leavitt path algebras induces an isomorphism of a certain quotient of algebraic filtered $K$ -theory and…

math.RA2019★ 1 cited

The talented monoid of a Leavitt path algebra

Roozbeh Hazrat, Huanhuan Li

There is a tight relation between the geometry of a directed graph and the algebraic structure of a Leavitt path algebra associated to it. In this note, we show a similar connectio…

math.RT2018

The injective and projective Leavitt complexes

Huanhuan Li

For a certain finite graph E, we consider the corresponding finite dimensional algebra A with radical square zero. An explicit compact generator for the homotopy category of acycli…

math.RA2018

$Z$ -graded rings as Cuntz-Pimsner rings

Lisa Orloff Clark, James Fletcher, Roozbeh Hazrat +1

Given a $Z$ -graded ring $A$ and a subring $R \subseteq A$ , it is natural to ask whether $A$ can be realised as the Cuntz-Pimsner ring of some $R$ -system. In this paper, we…

math.KT2018★ 1 cited

Homology of étale groupoids, a graded approach

Roozbeh Hazrat, Huanhuan Li

We introduce a graded homology theory for graded étale groupoids. For $Z$ -graded groupoids, we establish an exact sequence relating the graded zeroth-homology to non-graded…

math.RA2018★ 1 cited

Simple flat Leavitt path algebras are von Neumann regular

A. A. Ambily, Roozbeh Hazrat, Huanhuan Li

For a unital ring, it is an open question whether flatness of simple modules implies all modules are flat and thus the ring is von Neumann regular. The question was raised by Ramam…

math.RA2017

An explicit projective bimodule resolution of a Leavitt path algebra

Xiao-Wu Chen, Huanhuan Li, Zhengfang Wang

We construct an explicit projective bimodule resolution for the Leavitt path algebra of a row-finite quiver. We prove that the Leavitt path algebra of a row-countable quiver has Ho…

math.RA2017★ 1 cited

Graded Steinberg algebras and partial actions

Roozbeh Hazrat, Huanhuan Li

Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discre…

math.RA2017

Tate-Vogel and relative cohomologies of complexes with respect to cotorsion pairs

Jiangsheng Hu, Huanhuan Li, Jiaqun Wei +2

We study Tate-Vogel and relative cohomologies of complexes by applying the model structure induced by a complete hereditary cotorsion pair ($\A$, $\B$) of modules. We show first th…

math.KT2017★ 47 cited

Graded Steinberg algebras and their representations

Pere Ara, Roozbeh Hazrat, Huanhuan Li +1

We study the category of left unital graded modules over the Steinberg algebra of a graded ample Hausdorff groupoid. In the first part of the paper, we show that this category is i…

math.RT2016

The projective Leavitt complex

Huanhuan Li

Let Q be a finite quiver without sources, and A be the corresponding algebra with radical square zero. We construct an explicit compact generator for the homotopy category of acycl…

math.RT2015

The injective Leavitt complex

Huanhuan Li

For a finite quiver $Q$ without sinks, we consider the corresponding finite dimensional algebra $A$ with radical square zero. We construct an explicit compact generator for the hom…

math.RT2015

Applications of Exact Structures in Abelian Categories

Junfu Wang, Zhaoyong Huang

In an abelian category $A$ with small $Ext$ groups, we show that there exists a one-to-one correspondence between any two of the following: balanced pairs, subfunct…

math.RT2015★ 9 cited

Applications of Balanced Pairs

Huanhuan Li, Junfu Wang, Zhaoyong Huang

Let $(X$ , $Y)$ be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to $(X$ , $Y)$ , and then…

math.RT2015★ 10 cited

Relative Singularity Categories

Huanhuan Li, Zhaoyong Huang

We study the properties of the relative derived category $D_{C}^{b}$ ( $A$ ) of an abelian category $A$ relative to a full and additive subcategory $\mat…

Some more talents of the talented monoid of a higher-rank graph

How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings

The singularity category of an exact category applied to characterize Gorenstein schemes

2-recollements of singualrity categories and Gorenstein defect categories over triangular matrix algebras

Frobenius functors and Gorenstein projective precovers

Leavitt path algebras, B∞​-algebras and Keller's conjecture for singular Hochschild cohomology

When the Schur functor induces a triangle-equivalence between Gorenstein defect categories

A note on the core of Steinberg algebras

Gorenstein projective modules and recollements over triangular matrix rings

Graded K-Theory, Filtered K-theory and the classification of graph algebras

The talented monoid of a Leavitt path algebra

The injective and projective Leavitt complexes

Z-graded rings as Cuntz-Pimsner rings

Homology of étale groupoids, a graded approach

Simple flat Leavitt path algebras are von Neumann regular

An explicit projective bimodule resolution of a Leavitt path algebra

Graded Steinberg algebras and partial actions

Tate-Vogel and relative cohomologies of complexes with respect to cotorsion pairs

Graded Steinberg algebras and their representations

The projective Leavitt complex

The injective Leavitt complex

Applications of Exact Structures in Abelian Categories

Applications of Balanced Pairs

Relative Singularity Categories

Leavitt path algebras, $B_{\infty}$ -algebras and Keller's conjecture for singular Hochschild cohomology

Graded $K$ -Theory, Filtered $K$ -theory and the classification of graph algebras

$Z$ -graded rings as Cuntz-Pimsner rings