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Full-Text Articles in Algebra
Automorphisms Of A Generalized Quadrangle Of Order 6, Ryan Pesak
Automorphisms Of A Generalized Quadrangle Of Order 6, Ryan Pesak
Undergraduate Honors Theses
In this thesis, we study the symmetries of the putative generalized quadrangle of order 6. Although it is unknown whether such a quadrangle Q can exist, we show that if it does, that Q cannot be transitive on either points or lines. We first cover the background necessary for studying this problem. Namely, the theory of groups and group actions, the theory of generalized quadrangles, and automorphisms of GQs. We then prove that a generalized quadrangle Q of order 6 cannot have a point- or line-transitive automorphism group, and we also prove that if a group G acts faithfully on …
Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody
Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody
Undergraduate Honors Theses
A graph has quantum symmetry if the algebra associated with its quantum automorphism group is non-commutative. We study what quantum symmetry means and outline one specific method for determining whether a graph has quantum symmetry, a method that involves studying planar algebras and manipulating planar tangles. Modifying a previously used method, we prove that the 5-cycle has no quantum symmetry by showing it has the generating property.