Thesis (Ph. D.)--University of Oregon, 2008. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 105-107). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

Thesis (M.Sc.)(Mathematics)--University of Pretoria, 2004. / Title from opening screen (viewed March 11th, 2005). Includes summary. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1953. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 68-69).

Typescript. Includes vita and abstract. Includes bibliographical references (leaves 112-114) Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE / Bibliography: leaf 77. / by Devra Garfinkle. / Ph.D.

The work of this thesis focuses primarily on non-commutative algebras and actions of Hopf algebras. Specifically, we study the possible H-module algebra structures which can be imposed on path algebras of quivers, for a variety of Hopf algebras, H, and then given a possible action, classify the invariant ring. A Hopf algebra is a bialgebra (H, μ, η, ∆, ε) together with an antipode S : H → Hop which is compatible with the counit, ε, of H. A quiver is a directed graph, and the path algebra kQ of a quiver Q is a vector space where all the paths of the quiver form a basis, and multiplication is given by concatenation of paths whenever possible, and zero otherwise. In their paper, [9], Kinser and Walton classify Hopf actions of a specific family of Hopf algebras called a Taft algebras, T(n), on path algebras of loopless, finite, Schurian quivers. In this thesis, we extend their result to path algebras of any finite quiver and classify the invariant subring, kQT(n), in the case where the group like element g ∈ T(n) acts transitively on Q0. In the future, we hope that the ideas presented in this work extend to a classification of quantum groups, such as uq(sl2), acting on path algebras of finite quivers.

Thesis (Ph. D.)--University of Oregon, 2008. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 40-41). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

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The Khovanov{Lauda{Rouquier algebras Rn are a relatively new family of Z-graded algebras. Their cyclotomic quotients R n are intimately connected to a smaller family of algebras, the cyclotomic Hecke algebras H n of type A, via Brundan and Kleshchev's Graded Isomorphism Theorem. The study of representation theory of H n is well developed, partly inspired by the remaining open questions about the modular representations of the symmetric group Sn. There is a profound interplay between the representations for Sn and combinatorics, whereby each irreducible representation in characteristic zero can be realised as a Specht module whose basis is constructed from combinatorial objects. For R n , we can similarly construct their representations as analogous Specht modules in a combinatorial fashion. Many results can be lifted through the Graded Isomorphism Theorem from the symmetric group algebras, and more so from H n , to the cyclotomic Khovanov{Lauda{Rouquier algebras, providing a foundation for the representation theory of R n . Following the introduction of R n , Brundan, Kleshchev and Wang discovered that Specht modules over R n have Z-graded bases, giving rise to the study of graded Specht modules. In this thesis we solely study graded Specht modules and their irreducible quotients for R n . One of the main problems in graded representation theory of R n , the Graded Decomposition Number Problem, is to determine the graded multiplicities of graded irreducible R n -modules arising as graded composition factors of graded Specht modules. We rst consider R n in level one, which is isomorphic to the Iwahori{Hecke algebra of type A, and research graded Specht modules labelled by hook partitions in this context. In quantum characteristic two, we extend to R n a result of Murphy for the symmetric groups, determining graded ltrations of Specht modules labelled by hook partitions, whose factors appear as Specht modules labelled by two-part partitions. In quantum characteristic at least three, we determine an analogous R n -version of Peel's Theorem for the symmetric groups, providing an alternative approach to Chuang, Miyachi and Tan. We then study graded Specht modules labelled by hook bipartitions for R n in level two, which is isomorphic to the Iwahori{Hecke algebra of type B. In quantum characterisitic at least three, we completely determine the composition factors of Specht modules labelled by hook bipartitions for R n , together with their graded analogues.

by Lo Chui-sim. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 91-93). / Abstract --- p.i / Introcution --- p.1 / Chapter 1 --- Preliminaries --- p.3 / Chapter 1.1 --- Preliminaries on von-Neumann algebra --- p.3 / Chapter 1.2 --- Modular theory --- p.6 / Chapter 2 --- Abstract Lp Spaces --- p.10 / Chapter 2.1 --- "Preliminaries on dual action, dual weights and extended positive part" --- p.10 / Chapter 2.2 --- Abstract LP spaces associated with von-Neumann algebras --- p.20 / Chapter 2.3 --- "LP(M) is a Banach space for p E [1, ∞ ]" --- p.25 / Chapter 2.4 --- Independence of the choice of ψ --- p.32 / Chapter 3 --- Spatial Lp Spaces --- p.34 / Chapter 3.1 --- Definition and elementary properties of spatial derivative --- p.35 / Chapter 3.2 --- Modular properties of spatial derivatives --- p.47 / Chapter 3.3 --- Spatial Lp spaces --- p.51 / Chapter 4 --- LP Spaces constructed by using complex interpolation method --- p.60 / Chapter 4.1 --- The complex interpolation space --- p.60 / Chapter 4.2 --- LP space with respect to a faithful normal state --- p.71 / Chapter 4.3 --- LP spaces with respect to a normal faithful semifinite weight . . --- p.78 / Chapter 4.4 --- Equivalence to spatial LP spaces --- p.87 / Bibliography --- p.91