Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Oregon, 2005. / Typescript. Includes vita and abstract. Includes bibliographical references (leaf 61). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--University of Oregon, 2005. / Typescript. Includes vita and abstract. Includes bibliographical references (leaf 152). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on October 9, 2007) Vita. Includes bibliographical references.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-graduação em Matemática e Computação Científica, Florianópolis, 2010 / Made available in DSpace on 2012-10-25T09:04:07Z (GMT). No. of bitstreams: 1 276402.pdf: 394714 bytes, checksum: 81e09e3b56c695fa3d36e9da08fa6d48 (MD5) / O conceito de ações parciais vem sendo muito utilizado na teoria de C*-álgebras bem como em sistemas dinâmicos. Em 2005, Dokuchaev e Exel obtiveram resultados a respeito de ações parciais num contexto puramente algébrico onde mostraram, sob certas condições, a existência e a unicidade de uma ação envolvente. Nosso principal objetivo neste trabalho é mostrar a existência e a unicidade mencionadas acima. Para isso, desenvolvemos a teoria de álgebra dos multiplicadores e de ações parciais no contexto algébrico.

In this thesis we study subalgebras in free nilpotent and polynilpotent Lie algebras. Chapter 1 sets up the notation and includes definitions and elementary properties of free and certain reduced free Lie algebras that we use throughout this thesis. We also describe a Hall basis of a free Lie algebra as in [4] and a basis for a free polynilpotent Lie algebra which was developed in [24]. In Chapter 2 we first consider the class of nilpotency of subalbebras of free nilpotent Lie algebras starting with two-generator subalgebras. Then we study those subalgebras in a free nilpotent Lie algebra which, are themselves free nilpotent. We give necessary and sufficient conditions in the case of two-generator subalgebras. Chapter 3 extends the results obtained in Chapter 2 to the polynilpotent case. First we look at two-generator subalgebras of a free polynilpotent Lie algebra. Then we consider more general subalgebras. Finally we study those subalgebras which are themselves free polynilpotent and give necessary and sufficient conditions for two-generator subalgebras to be free polynilpotent. In Chapter 4 we first study certain properties of ideals in free, free nilpotent and free polynilpotent Lie algebras and establish the fact that in a free polynilpotent Lie algebra a nonzero ideal which is finitely-generated as a subalgebra must be equal to the whole algebra. Then we consider the quotient Lie algebra of a lower central term of a free Lie algebra by a term of the lower central series of an ideal. We then generalize the results to cover the free nilpotent and free polynilpotent cases. In the last section of Chapter 4 we consider ideals of free nilpotent (and later polynilpotent) Lie algebras as free nilpotent (polynilpotent) subalgebras and establish the fact that in most non-trivial cases such an ideal cannot be free nilpotent (polynilpotent). In the last chapter we consider the m+k-th term of the lower central series of a free Lie algebra as a subalgebra of the m-th term for m ⩽ k and generalize the results proved in [25]. We give reasons for the failure of these results in the case m > k.

Involutive automorphisms of complex affine Kac-Moody algebras (in particular, their conjugacy classes within the group of all automorphisms) and their compact real forms are studied, using the matrix formulation which was developed by Cornwell. The initial study of the a(1) series of affine untwisted Kac-Moody algebras is extended to include the complex affine untwisted Kac-Moody algebras B(1), C(1) and D(1). From the information obtained, explicit bases for real forms of these Kac-Moody algebras are then constructed. A scheme for naming some real forms is suggested. Further work is included which examines the involutive automorphisms and the real forms of A2(2)and the algebra G(1)2 (which is based upon an exceptional simple Lie algebra). The work involving the algebra A2(2)is part of work towards extending the matrix formulation to twisted Kac-Moody algebras. The analysis also acts as a practical test of this method, and from it we may infer different ways of using the formulation to eventually obtain a complete picture of the conjugacy classes of the involutive automorphisms of all the affine Kac-Moody algebras.

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O principal objetivo desta tese é um estudo de certas estruturas oriundas da ação de grupóides sobre álgebras. Especificamente tratamos do estudo de estruturas do tipo skew anel de grupóide. Dentre os principais resultados apresentados damos uma descrição estrutural intrínsica de um skew anel de grupóide, sob determinadas condições específicas, damos condições necessárias e suficientes para que um skew anel de grupóide seja uma extensão de Galois e apresentamos dois teoremas de dualidade do tipo Cohen-Montgomery para ações de grupóides. / The main purpose of this thesis is a study of certain structures arisen from the groupoid actions on algebras. Specifically, we deal with the study of structures of the type skew groupoid ring. Among the main results presented, we give an intrinsic structural description of the skew groupoid ring, under some specific conditions, we give necessary and sufficient conditions in order a skew groupoid ring be a Galois ex- tension, and we present two type Cohen-Montgomery duality theorems for groupoid actions.

Nesta dissertação realizamos um estudo sobre dois resultados clássicos da literatura referentes à dualidade para ação de álgebras de Hopf: a dualidade de Cohen-Montgomery e a dualidade de Blattner-Montgomery. No primeiro caso estendemos o resultado de Cohen-Montgomery ao contexto de ação parcial de grupos e no segundo caso estendemos o resultado de Blattner-Montgomery ao contexto de ação parcial de álgebras de Hopf. Esta dissertação foi elaborada tendo como base o artigo de C. Lomp, "Duality for partial groups actions", arXiv: 0711.0849v1[math.RA], 2007. / In this dissertation we are concerned with the following two classical results on duality: the Cohen-Montgomery duality and the Blattner-Montgomery duality; and we present their corresponding versions in the context of partial action of groups and partial actions of Hopf algebras, respectively. The subject of this dissertation is based on the C. Lomp’s paper: "Duality for partial group actions", arXiv: 0711.0849v1 [math.RA], 2007.