Huichi Huang

activity

20122026

most citedFaithful compact quantum group actions on connected compact metrizable spaces

28 citations · 34 across the 14 of their papers we have counts for

collaborators

15 papers

math.HO2026

A Concise Course in Galois Theory

Huichi Huang

Born from years of teaching undergraduate and graduate algebra courses at Chongqing University, this text is designed to introduce Galois theory while minimizing prerequisites. It…

math.FA2024

A Wiener-type theorem for arcs in the unit cirle

Huichi Huang

We prove a Wiener-type theorem for arcs in the unit circle which concerns express the measure of an arc in the unit circle via the measure's Fourier coefficients. Then we use it to…

math.OA2021

Amenable fusion algebraic actions of discrete quantum groups on compact quantum spaces

Xiao Chen, Debashish Goswami, Huichi Huang

In this paper, we introduce actions of fusion algebras on unital $C^{*}$ -algebras, and define amenability for fusion algebraic actions. Motivated by S.\ Neshveyev et al.'s work, cons…

math.DS2019

Strongly Independent Matrices and Rigidity of $\times A$ -Invariant Measures on $n$ -Torus

Huichi Huang, Hanfeng Li, Enhui Shi +1

We introduce the concept of strongly independent matrices over any field, and prove the existence of such matrices for certain fields and the non-existence for algebraically closed…

math.DS2018

Strongly Independent Matrices and Applications on the Rigidity of $A$ -Invariant Measures on $n$ -Torus

Huichi Huang, Enhui Shi, Hui Xu

We introduce the notion of strongly independent matrices and show the existence of strongly independent matrices in $G L (n, Z)$ over $Z^{n} ∖ {0}$ when $2 n + 1$ …

math.OA2016

Compact quantum stabilizer subgroups

Huichi Huang

We generalize the concept of stabilizer subgroups to compact quantum groups.

math.DS2016

Continuous $\times p, \times q$ -invariant measures on the unit circle

Huichi Huang

We express continuous $\times p, \times q$ -invariant measures on the unit circle via some simple forms. On one hand, a continuous $\times p, \times q$ -invariant measure is the weak-$…

math.OA2016

The quantum group fixing a sequence of finite subsets

Huichi Huang

Motivated by generalizing Szemerédi's theorem, we the elements in a discrete quantum group fixing a sequence of finite subsets and prove that the set of these elements is a quantum…

math.DS2016

Fourier coefficients of $\times p$ -invariant measures

Huichi Huang

We consider densities $D_{Σ} (A)$ , $D_{Σ} (A)$ and $D_{Σ} (A)$ for a subset $A$ of $N$ with respect to a sequence $Σ$ of finite subsets of $N$ and s…

math.CA2015

A generalized Fejér's theorem for locally compact groups

Huichi Huang

We prove a generalized Fejér's theorem for locally compact groups.

math.OA2015★ 3 cited

Mean ergodic theorem for amenable discrete quantum groups and a Wiener type theorem for compact metrizable groups

Huichi Huang

We prove a mean ergodic theorem for amenable discrete quantum groups. As an application, we prove a Wiener type theorem for continuous measures on compact metrizable groups.

math.OA2015

Ergodic invariant states and irreducible representations of crossed product $C^{*}$ -algebras

Huichi Huang, Jianchao Wu

Motivated by reformulating Furstenberg's $\times p, \times q$ conjecture via representations of a crossed product $C^{*}$ -algebra, we show that in a discrete $C^{*}$ -dynamical system $(…

math.DS2014

Equidistribution and measure rigidity under $\times p, \times q$

Huichi Huang

We show that equidistribution of irrational orbits on the unit circle implies Furstenberg's conjecture.

math.OA2012★ 3 cited

Invariant subsets under compact quantum group actions

Huichi Huang

We investigate compact quantum group actions on unital $C^{*}$ -algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact qua…

math.OA2012★ 28 cited

Faithful compact quantum group actions on connected compact metrizable spaces

Huichi Huang

We construct faithful actions of quantum permutation groups on connected compact metrizable spaces. This disproves a conjecture of Goswami.

A Concise Course in Galois Theory

A Wiener-type theorem for arcs in the unit cirle

Amenable fusion algebraic actions of discrete quantum groups on compact quantum spaces

Strongly Independent Matrices and Rigidity of ×A-Invariant Measures on n-Torus

Strongly Independent Matrices and Applications on the Rigidity of A-Invariant Measures on n-Torus

Compact quantum stabilizer subgroups

Continuous ×p,×q-invariant measures on the unit circle

The quantum group fixing a sequence of finite subsets

Fourier coefficients of ×p-invariant measures

A generalized Fejér's theorem for locally compact groups

Mean ergodic theorem for amenable discrete quantum groups and a Wiener type theorem for compact metrizable groups

Ergodic invariant states and irreducible representations of crossed product C∗-algebras

Equidistribution and measure rigidity under ×p,×q

Invariant subsets under compact quantum group actions

Faithful compact quantum group actions on connected compact metrizable spaces

Strongly Independent Matrices and Rigidity of $\times A$ -Invariant Measures on $n$ -Torus

Strongly Independent Matrices and Applications on the Rigidity of $A$ -Invariant Measures on $n$ -Torus

Continuous $\times p, \times q$ -invariant measures on the unit circle

Fourier coefficients of $\times p$ -invariant measures

Ergodic invariant states and irreducible representations of crossed product $C^{*}$ -algebras

Equidistribution and measure rigidity under $\times p, \times q$