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Structure and Representations for Electrical Lie Algebra of Type D_(5)

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Algebra Colloquium 2024年第2期31卷 271-284页

作者： Yulu Chen Ran Shen yucai su College of Science Donghua UniversityShanghai 201620China 不详

In this paper,we prove that the electrical Lie algebra e D_(5)is isomorphic to the semidirect product of sp_(4)and a 2-step nilpotent Lie ***,we classify the irreducible highest weight modules for e D_(5).

关键词： electrical Lie algebra 2-step nilpotent Lie algebra highest weight module

superhydrophobic surface-Assisted Preparation of Microspheres and supraparticles and Their Applications

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Nano-Micro Letters 2024年第4期16卷 110-138页

作者： Mengyao Pan Huijuan Shao Yue Fan Jinlong Yang Jiaxin Liu Zhongqian Deng Zhenda Liu Zhidi Chen Jun Zhang Kangfeng Yi yucai su Dehui Wang Xu Deng Fei Deng Institute of Fundamental and Frontier Sciences University of Electronic Science and Technology of ChinaChengdu 611731People’s Republic of China School of Materials Science and Engineering Sun Yat-Sen UniversityGuangzhou 510275People’s Republic of China Shenzhen Institute for Advanced Study University of Electronic Science and Technology of ChinaShenzhen 518110People’s Republic of China Pharmaceutical Glass Co.Ltd Zibo 256100People’s Republic of China Department of Nephropathy School of MedicineSichuan Provincial People’s HospitalUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China Department of Nephrology Sichuan Provincial People’s Hospital Jinniu HospitalChengdu Jinniu District People’s HospitalChengduPeople’s Republic of China

superhydrophobic surface(SHS) has been well developed, as SHS renders the property of minimizing the water/solid contact interface. Water droplets deposited onto SHS with contact angles exceeding 150°, allow them to retain spherical shapes, and the low adhesion of SHS facilitates easy droplet collection when tilting the substrate. These characteristics make SHS suitable for a wide range of applications. One particularly promising application is the fabrication of microsphere and supraparticle materials. SHS offers a distinct advantage as a universal platform capable of providing customized services for a variety of microspheres and supraparticles. In this review, an overview of the strategies for fabricating microspheres and supraparticles with the aid of SHS, including cross-linking process, polymer melting,and droplet template evaporation methods, is first presented. Then, the applications of microspheres and supraparticles formed onto SHS are discussed in detail, for example, fabricating photonic devices with controllable structures and tunable structural colors, acting as catalysts with emerging or synergetic properties, being integrated into the biomedical field to construct the devices with different medicinal purposes, being utilized for inducing protein crystallization and detecting trace amounts of analytes. Finally,the perspective on future developments involved with this research field is given, along with some obstacles and opportunities.

关键词： superhydrophobic surface Microspheres and supraparticles Photonic devices Catalysts Biomedical and trace detections

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Block型Lie超代数上的非权单模

中国科学：数学 2024年第1期54卷 39-58页

作者：苏育才岳晓青祝晓宇集美大学理学院厦门361021 同济大学数学科学学院上海200092 宁波大学数学与统计学院宁波315211

本文研究Block型Lie超代数S(q)上的一类非权模.本文构造和分类了Ramond-Block代数上秩为1的U(η)-自由模和Neveu-Schwarz-Block代数上秩为2的U(h)-自由模.同时也给出上述两类模成为单模的充要条件,并决定了它们的同构类.本文中的结果包... 详细信息

本文研究Block型Lie超代数S(q)上的一类非权模.本文构造和分类了Ramond-Block代数上秩为1的U(η)-自由模和Neveu-Schwarz-Block代数上秩为2的U(h)-自由模.同时也给出上述两类模成为单模的充要条件,并决定了它们的同构类.本文中的结果包含了一些已有结果.

关键词： Block型Lie超代数 Ramond-Block代数 Neveu-Schwarz-Block代数单模非权模

Dual Lie bialgebra structures of Poisson types

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Science China Mathematics 2015年第6期58卷 1151-1162页

作者： SONG Guang'Ai su yucai College of Mathematics and Information Science Shandong Institute of Business and Technology Department of Mathematics Tongji University

Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.

关键词： algebra Poisson commutative maximal associative infinite triangular polynomial multiplication subspace

Lie Bialgebras of a Family of Lie Algebras of Block Type

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Chinese Annals of Mathematics,Series B 2008年第5期29卷 487-500页

作者： Junbo LI yucai su Bin XIN Department of Mathematics Shanghai Jiao Tong University Shanghai 200240 China Department of Mathematics University of Science and Technology of China Hefei 230026 China

Lie bialgebra structures on a family of Lie algebras of Block type are shown to be triangular coboundary.

关键词： Lie bialgebras Yang-Baxter equation Lie algebra of Block type

Symmetric q-Deformed KP Hierarchy

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Chinese Annals of Mathematics,Series B 2015年第1期36卷 1-10页

作者： Kelei TIAN Jingsong HE yucai su School of Mathematics Hefei University of Technology Department of Mathematics Ningbo University Department of Mathematics Tongji University

Based on the analytic property of the symmetric q-exponent e_q(x),a new symmetric q-deformed Kadomtsev-Petviashvili(q-KP for short) hierarchy associated with the symmetric q-derivative operator α_q is ***,the symmetric q-CKP hierarchy and symmetric q-BKP hierarchy are *** authors also investigate the additional symmetries of the symmetric q-KP hierarchy.

关键词： q-Derivative Symmetric q-KP hierarchy Additional symmetries

Quantum Torus Lie Algebra in the q-Deformed Kadomtsev-Pe tv iashvili Sys tern

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Algebra Colloquium 2019年第4期26卷 579-588页

作者： Chuanzhong Li Xinyue Li Fushan Li yucai su School of Mathematics and Statistics Ningbo University NingboZhejiang 315211China College of Mathematics and Systems Science Shandong University of Science and Technology QingdaoShandong 266590China School of Mathematical Sciences Qufu Normal University QufuShandong 273165China 不详

Based on the symmetry of the Q-deformed Kadomtsev-Petviashvili(q-KP)hierarchy,which is a q-deformation of the KP hierarchy,we construct the quantum torus symmetry of the q-KP hierarchy,which further leads to the quantum torus constraint of its tau ***,we generalize the system to a multi-component q-KP hierarchy that also has the well-known ghost symmetry.

关键词： q-KP hierarchy Baker-Akhiezer function ghost symmetry quantum torus symmetry quantum torus constraint multi-component q-KP hierarchy

String Equations of the q-KP Hierarchy

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Chinese Annals of Mathematics,Series B 2011年第6期32卷 895-904页

作者： Kelei TIAN Jingsong HE yucai su Yi CHENG Wu Wen-Tsun Key Laboratory of Mathematics Department of Mathematics University of Science and Technology of China Hefei 230026 China Department of Mathematics Ningbo University Ningbo 315211 Zhejiang China Department of Mathematics Tongji University Shanghai 200092 China

Based on the Lax operator L and Orlov-Shulman's M operator,the string equations of the q-KP hierarchy are established from the special additional symmetry flows,and the negative Virasoro constraint generators {L-n,n ... 详细信息

关键词： q-KP hierarchy Additional symmetry String equations Virasoro constraints

Indecomposable modules of the intermediate series over W(a,b)

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Science China Mathematics 2014年第2期57卷 275-291页

作者： su yucai XU Ying YUE XiaoQing Department of Mathematics Tongji University Department of Mathematics Hefei University of Technology

For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=*** this paper,indecomposable modules of the intermediate series over W(a,b)are *** is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded ***,if a∈/Q,an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of Wk’s.

关键词： the algebra W(a b) the Virasoro algebra modules of the intermediate series