O objetivo principal desta tese e a construção do semigrupo inverso das classes de isomorfismo das extensões abelianas parciais de um anel comutativo. / The main purpose of this thesis is the construction of the inverse semigroup of the isomorphism classes of the partial abelian extensions of a commutative ring.

by Lo Kwok Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 97-98). / Chapter 1 --- Introduction --- p.2 / Chapter 1.1 --- Algebra and Coalgebra --- p.2 / Chapter 1.2 --- Bialgebra and Hopf Algebra --- p.18 / Chapter 1.3 --- Integral and Semisimplicity --- p.26 / Chapter 2 --- Order of antipode --- p.44 / Chapter 2.1 --- An Isomorphism between H and H* --- p.44 / Chapter 2.2 --- Opposite-co-opposite Hopf algebras --- p.50 / Chapter 2.3 --- Antipode has finite order --- p.57 / Chapter 3 --- Larson's Characters --- p.65 / Chapter 3.1 --- Theory of Characters for comodules --- p.66 / Chapter 3.2 --- Simple subcoalgebras under the action s2 --- p.75 / Chapter 4 --- Semisimple and Cosemisimple Hopf Algebras --- p.78 / Chapter 4.1 --- Trace functions for Hopf algebras --- p.78 / Chapter 4.2 --- Cosemisimple Hopf algebras are semisimple --- p.86 / Chapter 4.3 --- Semisimple Hopf algebras are involutory --- p.90

Pak Keung, Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 43). / Abstracts in English and Chinese. / Chapter 1 --- Preliminaries --- p.6 / Chapter 1.1 --- Definitions --- p.7 / Chapter 1.2 --- Topological Properties of the Structure Spaces of C*- Algebras --- p.14 / Chapter 1.3 --- "Topological Relations Between P(A), A and Prim(A)" --- p.17 / Chapter 2 --- Topological Properties of the Primal Ideal Spaces of C* - Algebras --- p.18 / Chapter 2.1 --- Topologies on Id(A) --- p.19 / Chapter 2.2 --- Minimal Primal Ideals and Their Topology --- p.31 / Chapter 3 --- Topological Representation of C*-Algebras --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- Main Results --- p.39 / Bibliography --- p.43

Neste trabalho discutimos a semissimplicidade de álgebras de Hopf finito-dimensionais e construímos o Duplo de Drinfeld D(H) de uma tal álgebra H. Além disso, apresentamos um resultado mostrando a equivalência entre as categorias de representações dos módulos sobre D(H) e dos módulos de Yetter-Drinfeld sobre Hcop. Como consequência deste estudo, apresentamos um resultado que caracteriza uma álgebra de Hopf quase triangular. / In this work we discuss the semisimplicity of some finite-dimensional Hopf Algebras and we set up the Drinfel’d double D(H) of such an algebra H. In addiction, we present a result showing the equivalence between the representation category of modules over D(H) and the Yetter-Drinfeld modules over Hcop. As a consequence of this, we present a result that features a quasitriangular Hopf algebra.

Bibliography: leaves 134-142.

Bibliography: leaves 54-55.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Sept. 18, 2008). PDF text: iv, 53 p. ; 293 K. UMI publication number: AAT 3297903. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis--M. Phil., University of Hong Kong, 1986.

published_or_final_version / Mathematics / Master / Master of Philosophy

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