位置：成果数据库 > 期刊 > 期刊详情页
A diagrammatic categorification of q-boson and q-fermion algebras
  • ISSN号：1674-1056
  • 期刊名称：《中国物理B：英文版》
  • 时间：0
  • 分类：O153.1[理学—数学;理学—基础数学] O572.2[理学—粒子物理与原子核物理;理学—物理]
  • 作者机构：[1]School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 相关基金：Project supported by the National Natural Science Foundation of China （Grant Nos. 10975102, 10871135, 11031005, and 11075014）. Acknowledgements The authors grately acknowledge the support of the Morningside Center of Mathematics and Prof. Wang Shi-Kun.
作者： 蔡立强[1], 林冰生[1], 吴可[1]
关键词： 子代数, 玻色子, 费米, 图表, FOCK态, 向量空间, 图形类, 代数和, categorification, q-boson algebra, q-Fock state, q-fermion algebra
中文摘要：

In this paper,we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra.We construct a graphical category corresponding to q-boson algebra.q-Fock states correspond to some kind of 1-morphisms,and the graded dimension of the graded vector space of 2-morphisms is exactly the inner product of the corresponding q-Fock states.We also find that this graphical category can be used to categorify q-fermion algebra.

英文摘要：

In this paper, we study the diagrammatic categorification of q-boson algebra and also q-fermion algebra. We construct a graphical category corresponding to q-boson algebra, q-Fock states correspond to some kind of 1-morphisms, and the graded dimension of the graded vector space of 2-morphisms is exactly the inner product of the corresponding q-Fock states. We also find that this graphical category can be used to categorify q-fermion algebra.

同期刊论文项目
量子场论和弦理论中的数学问题
期刊论文 80
旋量，超对称中的若干数学物理问题研究
期刊论文 12
广义纠缠相干态表象及其应用的研究
期刊论文 8
推广的协变延拓结构理论及其应用
期刊论文 19
同项目期刊论文
A diagrammatic categorification of q-boson and q-fermion algebras
One-dimensional multicomponent fermions with delta-function interaction in strong- and weak-coupling
Even and odd nonlinear charge coherent states and their nonclassical properties
A categorification of the boson oscillator
A diagrammatic categorification of the fermion algebra
Fermion Representation of Quantum Toroidal Algebra
The Fermion Representation of Quantum Toroidal Algebra on 3D Young Diagrams
Operator Product Formulas in the Algebraic Approach of the Refined Topological Vertex
CONSTRUCTION OF LAGRANGIAN SUBMANIFOLDS IN CPn
Colored Quantum Algebra and Its Bethe State
On Triple Product and Rational Solutions of Yang-Baxter Equation
Infinite-dimensional 3-algebra and integrable system
Off-diagonal Bethe ansatz and exact solution of a topological spin ring
A note on on-shell recursion relation of string amplitudes
Notes on symmetric BCJ numerator
Graphs, determinants and gravity amplitudes
<span style="font-family:SimSun;font-size:12pt;">Determinant formula for the partiti
学术:生命之树——忆侯伯宇先生
Super w(infinity) 3-algebra
量子场论大范围性质的研究工作介绍——纪念郭汉英研究员
On semi-classical topologically massive gravity in three dimensions
图，行列式和引力振福
An algebraic approach to BCJ numerators
The classification of two-loop integrand basis in pure four-dimension
<span style="font-family:SimSun;font-size:12pt;">Determinant representations of scal
SUPERLUMINAL NEUTRINOS FROM SPECIAL RELATIVITY WITH DE SITTER SPACETIME SYMMETRY
Free-field realization of the exceptional current superalgebra D(&#2;2, 1; α)k
Fermionic covariant prolongation structure theory for multidimensional super nonlinear evolution equ
(2+1)-Dimensional Integrable Heisenberg Supermagnet Model
Integrable Deformations of the (2+1)-Dimensional Heisenberg Ferromagnetic Model
Exact solution of the one-dimensional Hubbard model with arbitrary boundary megnetic fields
Off-diagonal Bethe ansatz solutions of the anisotropic spin-$\frac12$ chains with arbitrary boundary
The Construction of Dual-trace Factor in Yang-Mills Theory
Analytic structure of one-loop coefficients
Diagonal Slices of 3D Young Diagrams in the Approach of Maya Diagrams
An Introduction to On-shell Recursion Relations
Relations of loop partial amplitudes in gauge theory by Unitarity cut method
<span style="font-family:SimSun;font-size:12pt;">Thermodynamic limit of the off-diag
<span style="font-family:SimSun;font-size:12pt;">Nested off-diagonal Bethe ansatz an
<span style="font-family:SimSun;font-size:12pt;">Domain wall partition function of t
<span style="font-family:SimSun;font-size:12pt;">The classical exchange algebra of t
Categorification and Quasi-Hopf Algebras
ON SL(2, R) AND AdS GRAVITY
A categorification of the boson oscillator
<span style="font-family:SimSun;font-size:12pt;">Hamiltonian analysis of a Green-Sch
Determinant representations for scalar products of the XXZ Gaudin model with general boundary terms
A diagrammatic categorification of the fermion algebra
Schwarzschild de Sitter metric and inertial Beltrami coordinates
Monogamy deficit for quantum correlations in multipartite quantum system
Note on Construction of Dual-trace Factor in Yang-Mills Theory
Notes on teleportation in an expanding space
Dual-color decompositions at one-loop level in Yang-Mills theory
Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
Boundary Contributions Using Fermion Pair Deformation
BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
<span style="font-family:SimSun;font-size:12pt;">Spin-$\frac{1}{2}$ XYZ model revisi
<span style="font-family:SimSun;font-size:12pt;">Exact solution<span> </spa
<span style="font-family:SimSun;font-size:12pt;">Exact solution of the one-dimension
<span style="font-family:SimSun;font-size:12pt;">Direct Proof of Determinant Represe
<span style="font-family:SimSun;font-size:12pt;">Drinfeld twist and the domain wall
<span style="font-family:SimSun;font-size:12pt;">The second reference state and comp
<span style="color: rgb(102, 102, 102); line-height: 107%; font-family:;" ？？",&quo
Note on permutation sum of color-ordered gluon amplitudes
Drinfeld Twist and Symmetric Bethe Vectors of Open XYZ Chain with Non-Diagonal Boundary Terms
On Triple Product and Rational Solutions of Yang–Baxter Equation
Direct Proof of Determinant Representation for Scalar Products of the XXZ Gaudin Model with Generic Non-Diagonal Boundary Terms
量子仿射代数Uq（sln）的范畴化
A Categorification of Quantum sl2
Integrable Deformations of the （2＋1）-Dimensional Heisenberg Ferromagnetic Model Service and feedback Email this article to a colleague Add to Bookshelf Add to Citation Manager Cite This Article Email Alert Keywords Heisenberg ferromagnet model integrable deformation nonlinear Schr？dinger equation Authors YAN Zhao-Wen CHEN Min-Ru WU Ke ZHAO Wei-Zhong Integrable Deformations of the （2＋1）-Dimensional Heisenberg Ferromagnetic Model
Exact Polynomial Solutions of Schrdinger Equation with Various Hyperbolic Potentials
Fermionic covariant prolongation structure theory for supernonlinear evolution equation
Integrable Deformations of Heisenberg Supermagnetic Model
Categorification and Quasi-Hopf Algebras
SOLVING COLORED YANG-BAXTER EQUATION BY WU'S METHOD
Fermionic prolongation structure of the N=1 supersymmetric nonlocal gas equation
A Categorification of Quantum sl(2)
A categorification of the boson oscillator
A diagrammatic categorification of the fermion algebra
量子仿射代数Uq（sln）的范畴化
A Categorification of Quantum sl2
A Categorification of Quantum (sl(2))over-cap
Integrable Deformations of Heisenberg Supermagnetic Model
Categorification and Quasi-Hopf Algebras
A categorification of the boson oscillator
A diagrammatic categorification of the fermion algebra
量子仿射代数Uq（sln）的范畴化
离散的修正海森堡铁磁链方程的研究
各项异性的修正海森堡铁磁链方程的延拓结构
A Categorification of Quantum sl2
Integrable Deformations of the （2＋1）-Dimensional Heisenberg Ferromagnetic Model Service and feedback Email this article to a colleague Add to Bookshelf Add to Citation Manager Cite This Article Email Alert Keywords Heisenberg ferromagnet model integrable deformation nonlinear Schr？dinger equation Authors YAN Zhao-Wen CHEN Min-Ru WU Ke ZHAO Wei-Zhong Integrable Deformations of the （2＋1）-Dimensional Heisenberg Ferromagnetic Model
期刊信息
  • 《中国物理B：英文版》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国物理学会和中国科学院物理研究所
  • 主编：欧阳钟灿
  • 地址：北京 中关村 中国科学院物理研究所内
  • 邮编：100080
  • 邮箱：
  • 电话：010-82649026 82649519
  • 国际标准刊号：ISSN：1674-1056
  • 国内统一刊号：ISSN：11-5639/O4
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 被引量:406