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- Yang-Baxter equation (2)
- Authomorphism rigidity of graphs (1)
- Binormal operator (1)
- Complex symmetric operator (1)
- Dynamical reflection equation (1)
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- Hamiltonian Lie algebras (1)
- Idempotent (1)
- Intertwining operators (1)
- K-colorability (1)
- Lie algebras (1)
- Nilpotent operator (1)
- Normal operator (1)
- Partial isometry (1)
- Polynomial method (1)
- Quantization (1)
- Quantum superintegrable systems (1)
- Quasi-trigonometric solutions (1)
- Unique Hamiltonicity (1)
Articles 1 - 6 of 6
Full-Text Articles in Algebra
Review: The Semi-Dynamical Reflection Equation: Solutions And Structure Matrices, Gizem Karaali
Review: The Semi-Dynamical Reflection Equation: Solutions And Structure Matrices, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Recognizing Graph Theoretic Properties With Polynomial Ideals, Jesus A. De Loera, Christopher J. Hillar, Peter N. Malkin, Mohamed Omar
Recognizing Graph Theoretic Properties With Polynomial Ideals, Jesus A. De Loera, Christopher J. Hillar, Peter N. Malkin, Mohamed Omar
All HMC Faculty Publications and Research
Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of the polynomial method and show how the algorithmic theory of polynomial ideals can be used to detect k-colorability, unique Hamiltonicity, and automorphism rigidity of graphs. Our techniques are diverse and involve Nullstellensatz certificates, linear algebra over finite fields, Gröbner bases, toric algebra, convex programming, and real algebraic geometry.
Some New Classes Of Complex Symmetric Operators, Stephan Ramon Garcia, Warren R. Wogen
Some New Classes Of Complex Symmetric Operators, Stephan Ramon Garcia, Warren R. Wogen
Pomona Faculty Publications and Research
We say that an operator $T \in B(H)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:H\to H$ so that $T = CT^*C$. We prove that binormal operators, operators that are algebraic of degree two (including all idempotents), and large classes of rank-one perturbations of normal operators are complex symmetric. From an abstract viewpoint, these results explain why the compressed shift and Volterra integration operator are complex symmetric. Finally, we attempt to describe all complex symmetric partial isometries, obtaining the sharpest possible statement given only the data $(\dim \ker T, \dim \ker T^*)$.
Review: Classification Of Quasi-Trigonometric Solutions Of The Classical Yang-Baxter Equation, Gizem Karaali
Review: Classification Of Quasi-Trigonometric Solutions Of The Classical Yang-Baxter Equation, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Intertwining Symmetry Algebras Of Quantum Superintegrable Systems, Gizem Karaali
Review: Intertwining Symmetry Algebras Of Quantum Superintegrable Systems, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Quantization Of Hamiltonian-Type Lie Algebras, Gizem Karaali
Review: Quantization Of Hamiltonian-Type Lie Algebras, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.