No description available.

Thesis (doctoral)--Rheinische Friedrich-Wilhelm-Universität Bonn, 1985. / Bibliography: p. 45-49.

No description available.

No description available.

iii, 66 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1976

Thesis (Ph.D.) -- University of Adelaide, Department of Pure Mathematics, 1976.

No description available.

In this thesis, we construct Chevalley groups over arbitrary fields. The construction is based on the properties of semi-simple complex Lie algebras, the existence of Chevalley bases and notion of universal enveloping algebras. Using integral lattices in universal enveloping algebras and integral properties of Chevalley bases, we present a method which produces, for any complex simple Lie group, an analogous group over an arbitrary field.

The odd symplectic Grassmannian IG := IG(k, 2n + 1) parametrizes k dimensional subspaces of C^2n+1 which are isotropic with respect to a general (necessarily degenerate) symplectic form. The odd symplectic group acts on IG with two orbits, and IG is itself a smooth Schubert variety in the submaximal isotropic Grassmannian IG(k, 2n + 2). We use the technique of curve neighborhoods to prove a Chevalley formula in the equivariant quantum cohomology of IG, i.e. a formula to multiply a Schubert class by the Schubert divisor class. This generalizes a formula of Pech in the case k = 2, and it gives an algorithm to calculate any quantum multiplication in the equivariant quantum cohomology ring. / Ph. D. / The thesis studies a problem in the general area of Combinatorial Algebraic Geometry. The goal of Algebraic Geometry is to study solutions to systems to polynomial equations. Such systems are ubiquitous in scientific research. We study a problem in enumerative geometry on a space called the odd symplectic Grassmannian. The problem seeks to find the number of curves which are incident to certain subspaces of the given Grassmannian. Due to subtle geometric considerations, the count is sometimes virtual, meaning that some curves need to be counted negatively. The rigorous context of such questions is that of Gromov-Witten theory, a subject with roots in physics. Our space affords a large number of symmetries, and the given counting problems translate into significant amount of combinatorial manipulations. The main result in the dissertation is a combinatorial algorithm to perform the virtual curve counting in the odd-symplectic Grassmannian.

Orientadores: Adriano Adrega de Moura, Marcos Benevenuto Jardim / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-09-11T21:13:21Z (GMT). No. of bitstreams: 1 Macedo_TiagoRodrigues_M.pdf: 809265 bytes, checksum: 0f4ecb72bd6a8b221a3514e62b63fd41 (MD5) Previous issue date: 2009 / Resumo: Apresentaremos resultados relacionando a álgebra de distribuições de grupos de Chevalley com as chamadas hiperálgebras. Estas últimas são álgebras de Hopf construídas por redução módulo p da forma integral de Kostant para álgebras de Lie simples. Em seguida, tentamos, a partir de uma certa classe de álgebras de Hopf, a saber, álgebras de Hopf que são álgebras de distribuições de grupos algébricos, reconstruir esses grupos algébricos. / Abstract: We present some results which relate the algebra of distributions of a Chevalley group and the so called hyperalgebras. The latter are Hopf algebras obtained by reduction modulo p of the Kostant integral form of a simple Lie algebra. Then we try to rebuild algebraic groups from Hopf algebras which are their algebras of distribution. / Mestrado / Algebra / Mestre em Matemática