Browsing by Author "Dr. Tom Lada, Committee Member"

Now showing 1 - 4 of 4

Algorithms for Computing Restricted Root Systems and Weyl Groups
(2006-05-04) Cicco, Tracey Martine Westbrook; Dr. Aloysius Helminck, Committee Chair; Dr. Ernest Stitzinger, Committee Member; Dr. Tom Lada, Committee Member; Dr. Amassa Fauntleroy, Committee Member
While the computational packages LiE, Gap4, Chevie, and Magma are sufficient for work with Lie Groups and their corresponding Lie Algebras, no such packages exist for computing the k-structure of a group or the structure of symmetric spaces. My goal is to examine the k-structure of groups and the structure of symmetric spaces and arrive at various algorithms for computing in these spaces.
On the classification of orbits of minimal parabolic k-subgroups acting on symmetric k-varieties of SL(n,k)
(2008-04-25) Beun, Stacy L.; Dr. Tom Lada, Committee Member; Dr. Ernest Stitzinger, Committee Member; Dr. Aloysius Helminck, Committee Chair; Dr. Amassa Fauntleroy, Committee Member
On the Solvability of Nonlinear Discrete Multipoint Boundary Value Problems
(2007-04-17) Taylor, Padraic Whittingham; Dr. Jesus Rodriguez, Committee Chair; Dr. James Selgrade, Committee Member; Dr. Tom Lada, Committee Member; Dr. Kailash Misra, Committee Member
In this manuscript we study nonlinear, discrete, multipoint boundary value problems. We investigate two types of problems. We first consider scalar, nonlinear, multipoint boundary value problems. We provide sufficient conditions for the existence of solutions. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems. [8,9]. We also study weakly nonlinear, discrete systems. We provide sufficient conditions for the existence of solutions and we present a qualitative analysis of the way the solutions depend on the parameter.
Relationship Between Symmetric and Skew-Symmetric Bilinear Forms on V=kn and Involutions of SL(n,k) and SO(n,k,beta)
(2003-10-22) Dometrius, Christopher; Dr. Aloysius Helminck, Committee Chair; Dr. Naihuan Jing, Committee Member; Dr. Tom Lada, Committee Member; Dr. Ernest Stitzinger, Committee Member
In this paper, we show how viewing involutions on matrix groups as having been induced by a given non-degenerate symmetric or skew-symmetric bilinear form on the vector space of corresponding dimension can lead to a classification up to isomorphism of the resulting reductive symmetric space in the group setting. We establish a direct link between bilinear algebraic properties of the vector space V=kˆn for an arbitrary field k of characteristic not 2 and involutions of the matrix group G, where G is a subgroup of GL(n,k). Symmetric spaces are defined in terms of involutions, and the development of this classification theory which classifies the involutions also classifies the symmetric spaces coming from these involutions. We classify all involutions on SL(n,k) and develop important foundations for a full classification of the involutons of SO(n,k,beta) where beta is any non-degenerate symmetric bilinear form. We prove that all involutions of SO(n,k,beta) are inner when n is odd. Additionally, we provide criteria for the matrix which gives the conjugation that is the inner involution of SO(n,k,beta), which covers all involutions when n is odd and all involutions which can be written as conjugations when n is even, a fact which is proven in this thesis.