arXiv subjects

Huan Jia

Publications and source records attributed to Huan Jia.

10 recordsLinked to original sources

arXiv2026

A Noetherian Hopf algebra is affine iff its Hopf coradical is affine

Let $\K$ denote a field. Extending the structural frameworks established in \cite{JZ2025-2}, this paper introduces novel techniques utilizing non-commutative reduction orders, factorization theory, and the generalized lifting methodology. We establish a definitive necessary and sufficient criterion for the affineness of Noetherian Hopf algebras, thereby providing a significant advancement toward resolving the long-standing Wu--Zhang question \cite{WZ2003}. Specifically, we prove that a left or right Noetherian Hopf algebra over $\K$ is affine if and only if its Hopf coradical is affine. This characterization fundamentally concentrates the burden of verification onto the first filtration step, yielding a criterion that is structurally transparent and highly operational. To establish necessity, we provide an essential intrinsic result demonstrating that the Hopf coradical of an affine Hopf algebra inherits the property of being affine. Furthermore, as direct applications of this equivalence, we prove that a left or right Noetherian Hopf algebra $H$ is affine provided that its coradical $H_{(0)}$ forms a subalgebra (the dual Chevalley property), its coradical $H_{(0)}$ is cocommutative, or its Hopf coradical $H_{[0]}$ is commutative.

math.RA↗

arXiv2025

Noetherian pointed Hopf algebras are affine

Let $k$ be a field. In this paper, we introduce the notions of $\textit{reduction order}$ and $\textit{reduction-factorization}$ on words, and use them to show that any right or left Noetherian pointed Hopf algebra over $k$ is affine. This result offers a partial affirmative answer to the classical affineness question for Noetherian Hopf algebras posed by Wu and Zhang \cite{WZ2003}. For a pointed Hopf algebra $H$ over $k$, we construct a well-ordered set $X$ such that: (1) $H$ is generated, as an algebra, by the subset $X_I$ of irreducible letters (with respect to the reduction order); and (2) $X_I$ is finite whenever $H$ is right Noetherian.

math.QA↗

arXiv2025

Conceptual Design of the Muonium-to-Antimuonium Conversion Experiment (MACE)

The spontaneous conversion of muonium to antimuonium is one of the interesting charged lepton flavor violation phenomena offering a sensitive probe of potential new physics and serving as a tool to constrain the parameter space beyond the Standard Model. The Muonium-to-Antimuonium Conversion Experiment (MACE) is designed to utilize a high-intensity muon beam, a Michel electron magnetic spectrometer, a positron transport system, and a positron detection system, to either discover or constrain this rare process with a conversion probability of $\mathcal{O}(10^{-13})$. This article presents an overview of the theoretical framework as well as a detailed description of the experimental design for the search for muonium-to-antimuonium conversion.

hep-ex↗

arXiv2025

High-Precision Physics Experiments at Huizhou Large-Scale Scientific Facilities

In response to the capabilities presented by the High-Intensity Heavy Ion Accelerator Facility (HIAF) and the Accelerator-Driven Subcritical System (CiADS), as well as the proposed Chinese Advanced Nuclear Physics Research Facility (CNUF), we are assembling a consortium of experts in relevant discipline--both domestically and internationally--to delineate high-precision physics experiments that leverage the state-of-the-art research environment afforded by CNUF. Our focus encompasses six primary domains of inquiry: hadron physics--including endeavors such as the super eta factory and investigations into light hadron structures; muon physics; neutrino physics; neutron physics; the testing of fundamental symmetries; and the exploration of quantum effects within nuclear physics, along with the utilization of vortex accelerators. We aim to foster a well-rounded portfolio of large, medium, and small-scale projects, thus unlocking new scientific avenues and optimizing the potential of the Huizhou large scientific facility. The aspiration for international leadership in scientific research will be a guiding principle in our strategic planning. This initiative will serve as a foundational reference for the Institute of Modern Physics in its strategic planning and goal-setting, ensuring alignment with its developmental objectives while striving to secure a competitive edge in technological advancement. Our ambition is to engage in substantive research within these realms of high-precision physics, to pursue groundbreaking discoveries, and to stimulate progress in China's nuclear physics landscape, positioning Huizhou as a preeminent global hub for advanced nuclear physics research.

hep-ph↗

arXiv2025

Affineness on Noetherian graded rings, algebras and Hopf algebras

In this note, we show that every Noetherian graded ring with an affine degree zero part is affine. As a result, a Noetherian graded Hopf algebra whose degree zero component is a commutative or a cocommutative Hopf subalgebra is affine. Moreover, we show that the braided Hopf algebra of a Noetherian graded Hopf algebra is affine.

math.RA↗

arXiv2023

Towards a high-intensity muon source at CiADS

The proposal of a high-intensity muon source driven by the CiADS linac, which has the potential to be one of the state-of-the-art facilities, is presented in this paper. We briefly introduce the development progress of the superconducting linac of CiADS. Then the consideration of challenges related to the high-power muon production target is given and the liquid lithium jet muon production target concept is proposed, for the first time. The exploration of the optimal target geometry for surface muon production efficiency and the investigation into the performance of liquid lithium jet target in muon rate are given. Based on the comparison between the liquid lithium jet target and the rotation graphite target, from perspectives of surface muon production efficiency, heat processing ability and target geometry compactness, the advantages of the new target concept are demonstrated and described comprehensively. The technical challenges and the feasibility of the free-surface liquid lithium target are discussed.

physics.acc-ph↗

arXiv2023

Noncommutative binomial theorem, shuffle type polynomials and Bell polynomials

In this paper we use the Lyndon-Shirshov basis to study the shuffle type polynomials. We give a free noncommutative binomial (or multinomial) theorem in terms of the Lyndon-Shirshov basis. Another noncommutative binomial theorem given by the shuffle type polynomials with respect to an adjoint derivation is established. As a result, the Bell differential polynomials and the $q$-Bell differential polynomials can be derived from the second binomial theorem. The relation between the shuffle type polynomials and the Bell differential polynomials is established. Finally, we give some applications of the free noncommutative binomial theorem including application of the shuffle type polynomials to bialgebras and Hopf algebras.

math.CO↗

arXiv2023

Quotient Hopf algebras of the free bialgebra with PBW bases and GK-dimensions

Let $\mathbb{K}$ be a field. We study the free bialgebra $\mathcal{T}$ generated by the coalgebra $C=\mathbb{K} g \oplus \mathbb{K} h$ and its quotient bialgebras (or Hopf algebras) over $\mathbb{K}$. We show that the free noncommutative Faà di Bruno bialgebra is a sub-bialgebra of $\mathcal{T}$, and the quotient bialgebra $\overline{\mathcal{T}}:=\mathcal{T}/(E_α|~α(g)\ge 2)$ is an Ore extension of the well-known Faà di Bruno bialgebra. The image of the free noncommutative Faà di Bruno bialgebra in the quotient $\overline{\mathcal{T}}$ gives a more reasonable non-commutative version of the commutative Faà di Bruno bialgebra from the PBW basis point view. If char $\mathbb{K}=p>0$, we obtain a chain of quotient Hopf algebras of $\overline{\mathcal{T}}$: $\overline{\mathcal{T}} \twoheadrightarrow \overline{\mathcal{T}}_{n}\twoheadrightarrow \overline{\mathcal{T}}_{n}'(p)\twoheadrightarrow \overline{\mathcal{T}}_{n}(p)\twoheadrightarrow \overline{\mathcal{T}}_{n}(p;d_{1}) \twoheadrightarrow \ldots \twoheadrightarrow \overline{\mathcal{T}}_{n}(p;d_{j},d_{j-1},\ldots,d_{1}) \twoheadrightarrow \ldots \twoheadrightarrow \overline{\mathcal{T}}_{n}(p;d_{p-2},d_{p-3},\ldots,d_{1})$ with finite GK-dimensions. Furthermore, we study the homological properties and the coradical filtrations of those quotient Hopf algebras.

math.QA↗

arXiv2022

$\rm ^{83}Rb$/$\rm ^{83m}Kr$ production and cross-section measurement with 3.4 MeV and 20 MeV proton beams

$\rm ^{83m}Kr$, with a short lifetime, is an ideal calibration source for liquid xenon or liquid argon detectors. The $\rm ^{83m}Kr$ isomer can be generated through the decay of $\rm ^{83} Rb$ isotope which is usually produced by proton beams bombarding natural krypton atoms. In this paper, we report a successful production of $\rm ^{83}Rb/^{83m}Kr$ with a proton beam energy of 3.4 MeV, and the first measurement of the production rate with such low energy proton beams. Another production attempt is performed using the newly available 20 MeV proton beam in China, and the measured production rate is consistent with previous measurements. The produced $\rm ^{83m}Kr$ source has been successfully injected into the PandaX-II liquid xenon detector, yielding enough statistics for detector calibration.

nucl-ex↗

arXiv2014

Research on the Design and Simulation of the CSRe Stochastic Cooling System

Stochastic cooling, as the different cooling mechanism from electron cooling, is designed and constructed on CSRe (experimental Cooling Storage Ring) in HIRFL (Heavy Ion Research Facility in Lanzhou) at present. The beam extracted from CSRm (main Cooling Storage Ring) is injected into the CSRe, and then the secondary beam with large momentum spread and large emittance is produced at the internal target area. This paper is designed to optimize the lattice of CSRe in order to satisfy the requirement of stochastic cooling system. Particle Tracking Method is used and both transverse and longitudinal simulation is made on the basis of the designed lattice. The results indicate that stochastic cooling is suitable for beam cooling with larger momentum spread or larger emittance, and cooling rate is preliminarily confirmed.

physics.acc-ph↗