Department of Mathematicshttp://hdl.handle.net/1957/137372017-08-11T00:27:05Z2017-08-11T00:27:05ZSubalgebras of the Split OctonionsBentz, Lidahttp://hdl.handle.net/1957/617552017-08-09T17:26:38Z2017-06-06T00:00:00ZSubalgebras of the Split Octonions
Bentz, Lida
We classify the subalgebras of the split octonions, paying particular attention to the null subalgebras and their extensions.
June 17: 2017
2017-06-06T00:00:00ZClassifying Octonionic-Linear OperatorsPutnam, Alexanderhttp://hdl.handle.net/1957/617072017-07-05T18:19:59Z2017-07-05T00:00:00ZClassifying Octonionic-Linear Operators
Putnam, Alexander
The goal of this paper is to classify linear operators with octonionic coefficients and octonionic variables. While building up to the octonions we also classify linear operators over the quaternions and show how to relate the linear operators over the quaternions and octonions to matrices. We also construct a basis of linear operators that maps to the canonical basis of matrices for each space. Finally, we discuss automorphisms of the octonions, a special subset of the linear operators.
June 2017
2017-07-05T00:00:00ZKACZMARZ AND RANDOMIZED KACZMARZ METHODAbubakari, Nurideenhttp://hdl.handle.net/1957/614792017-06-20T21:29:29Z2017-06-20T00:00:00ZKACZMARZ AND RANDOMIZED KACZMARZ METHOD
Abubakari, Nurideen
2017
2017-06-20T00:00:00ZA New Algorithm for Computing the Veech Group of a Translation SurfaceEdwards, Brandon (Brandon Gary)http://hdl.handle.net/1957/606332017-04-13T20:35:29Z2017-03-17T00:00:00ZA New Algorithm for Computing the Veech Group of a Translation Surface
Edwards, Brandon (Brandon Gary)
We give a new characterization of elements in the Veech group of a translation surface. This provides a computational test for Veech group membership. We use this computational test in an algorithm that detects when the Veech group is a lattice (has co-finite area), and in this case computes a fundamental polygon for the action of the Veech group on the hyperbolic plane. A standard result, essentially due to Poincaré, provides that a complete set of generators for the Veech group can then be obtained from the side pairings associated to this fundamental polygon.
Our approach introduces a new computational framework used to formulate a membership criterion for the Veech group of a compact translation surface (X,ω). We represent (X,ω) on a certain non-compact translation surface O that can be used to represent any translation surface within the SL(2,ℝ) orbit of the translation equivalence class of (X,ω). The surface O has an easily computed SL(2,ℝ)-action. When this action is restricted to the translation surface representations mentioned above, it corresponds to the usual SL(2,ℝ)-action on the set of equivalence classes of translation surfaces. The Veech group of a compact translation surface is therefore the stabilizer of its representation on O.
Graduation date: 2017
2017-03-17T00:00:00Z