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Full-Text Articles in Physical Sciences and Mathematics
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 …
Examining Factors Using Standard Subspaces And Antiunitary Representations, Paul Anderson
Examining Factors Using Standard Subspaces And Antiunitary Representations, Paul Anderson
Undergraduate Honors Theses
In an effort to provide an axiomization of quantum mechanics, John von Neumann and Francis Joseph Murray developed many tools in the theory of operator algebras. One of the many objects developed during the course of their work was the von Neumann algebra, originally called a ring of operators. The purpose of this thesis is to give an overview of the classification of elementary objects, called factors, and explore connections with other mathematical objects, namely standard subspaces in Hilbert spaces and antiunitary representations. The main results presented here illustrate instances of these interconnections that are relevant in Algebraic Quantum Field …