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.

The central objects of study in this thesis are quantized coordinate algebras. These algebras originated in the 1980s in the work of Drinfeld and Jumbo and are noncommutative analogues of coordinate rings of algebraic varieties. The organic nature by which these algebras arose is of great interest to algebraists. In particular, investigating ring theoretic properties of these noncommutative algebras in comparison to the properties already known about their classical (commutative) counterparts proves to be a fruitful process. The prime spectrum of an algebra has always been seen as an important key to understanding its fundamental structure. The search for prime spectra is a central focus of this thesis. Our focus is mainly on Quantum Grassmannian subalgebras of quantized coordinate rings of Matrices of size m x n (denoted Oq(Mm;n)). Quantum Grassmannians of size m x n are denoted Gq(m; n) and are the subalgebras generated by the maximal quantum minors of Oq(Mm;n). In Chapter 2 we look at the simplest interesting case, namely the 2 x 4 Quantum Grassmannian (Gq(2; 4)), and we identify the H-primes and automorphism group of this algebra. Chapter 3 begins with a very important result concerning the dehomogenisation isomorphism linking Gq(m; n) and Oq(Mm;n¡m). This result is applied to help to identify H-prime spectra of Quantum Grassmannians. Chapter 4 focuses on identifying the number of H-prime ideals in the 2xn Quan- tum Grassmannian. We show the link between Cauchon fillings of subpartitions and H-prime ideals. In Chapter 5, we look at methods of ordering the generating elements of Quantum Grassmannians and prove the result that Quantum Grassmannians are Quantum Graded Algebras with a Straightening Law is maintained on using one of these alternative orderings. Chapter 6 looks at the Poisson structure on the commutative coordinate ring, G(2; 4) encoded by the noncommutative quantized algebra Gq(2; 4). We describe the symplectic ideals of G(2; 4) based on this structure. Finally in Chapter 7, we present an analysis of the 2 x 2 Reflection Equation Algebra and its primes. This algebra is obtained from the quantized coordinate ring of 2 x 2 matrices, Oq(M2;2).

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 56).

Thesis (Ph. D.)--University of Oregon, 2003. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 106-108). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Mathematics." Includes bibliographical references (p. 82-83).

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

Univ., Habil.-Schr. u.d.T.: Gohm, Rolf: Elements of a spatial theory for noncommutative stationary processes with discrete time index--Greifswald, 2002. / Literaturverz. S. [165] - 168.

Thesis (Ph. D.)--University of Oregon, 1999. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 103-105). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p9947969.

Thesis (Ph. D.)--University of Oregon, 2005. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 48-49). Also available for download via the World Wide Web; free to University of Oregon users.

Bibliography: p. 155-161.