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Algebra Commons

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Articles 1 - 6 of 6

Full-Text Articles in Algebra

Review: The Semi-Dynamical Reflection Equation: Solutions And Structure Matrices, Gizem Karaali Jan 2010

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 Jan 2010

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 Jan 2010

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 Jan 2010

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 Jan 2010

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 Jan 2010

Review: Quantization Of Hamiltonian-Type Lie Algebras, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.