Spelling suggestions: "subject:"artin algebra."" "subject:"crtin algebra.""
1 |
Three dimensional FC Artin groups are CAT(0) /Bell, Robert William, January 2003 (has links)
Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains viii, 103 p.; also includes graphics Includes bibliographical references (p. 102-103). Available online via OhioLINK's ETD Center
|
2 |
A class of Gorenstein Artin algebras of embedding dimension fourEl Khoury, Sabine, January 2007 (has links)
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 March 20, 2009) Vita. Includes bibliographical references.
|
3 |
Homology of Coxeter and Artin groupsBoyd, Rachael January 2018 (has links)
We calculate the second and third integral homology of arbitrary finite rank Coxeter groups. The first of these calculations refines a theorem of Howlett, the second is entirely new. We then prove that families of Artin monoids, which have the braid monoid as a submonoid, satisfy homological stability. When the K(π,1) conjecture holds this gives a homological stability result for the associated families of Artin groups. In particular, we recover a classic result of Arnol'd.
|
4 |
Uniform modules over serial rings.Lelwala, Menaka. Muller, Bruno, J. Unknown Date (has links)
Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 57-03, Section: B, page: 1845. Adviser: B. J. Mueller.
|
5 |
Cohomology of finite and affine type Artin groups over Abelian representation /Callegaro, Filippo. January 2009 (has links)
Originally presented as the author's Thesis (Ph. D.)--Scuola normale superiore Pisa. / Includes bibliographical references (p. [125]-131) and index.
|
6 |
Representation theory of the diagram An over the ring k[[x]]Corwin, Stephen P. January 1986 (has links)
Fix R = k[[x]]. Let Q<sub>n</sub> be the category whose objects are ((M₁,...,M<sub>n</sub>),(f₁,...,f<sub>n-1</sub>)) where each M<sub>i</sub> is a free R-module and f<sub>i</sub>:M<sub>i</sub>⟶M<sub>i+1</sub> for each i=1,...,n-1, and in which the morphisms are the obvious ones. Let β<sub>n</sub> be the full subcategory of Ω<sub>n</sub> in which each map f<sub>i</sub> is a monomorphism whose cokernel is a torsion module. It is shown that there is a full dense functor Ω<sub>n</sub>⟶β<sub>n</sub>. If X is an object of β<sub>n</sub>, we say that X <u>diagonalizes</u> if X is isomorphic to a direct sum of objects ((M₁,...,M<sub>n</sub>),(f₁,...,f<sub>n-1</sub>)) in which each M<sub>i</sub> is of rank one. We establish an algorithm which diagonalizes any diagonalizable object X of β<sub>n</sub>, and which fails only in case X is not diagonalizable.
Let Λ be an artin algebra of finite type. We prove that for a fixed C in mod(Λ) there are only finitely many modules A in mod(Λ) (up to isomorphism) for which a short exact sequence of the form 0⟶A⟶B⟶C⟶0 is indecomposable. / Ph. D. / incomplete_metadata
|
7 |
Graded artin algebras, coverings and factor ringsWeaver, Martha Ellen January 1986 (has links)
Let (Γ,ρ) be a directed graph with relations. Let F: Γ’ → Γ be a topological covering. It is proved in this thesis that there is a set of relations ρ̅ on Γ such that the category of K-respresentations of Γ’ whose images under the covering functor satisfy ρ is equivalent to the category of finite-dimensional, grades KΓ/<ρ̅>-modules. If Γ’ is the universal cover of Γ, then this category is called the category of unwindable KΓ/<ρ>-modules. For arrow unique graphs it is shown that the category of unwindable KΓ/<ρ>-modules does not depend on <ρ>. Also, it is shown that for arrow unique graphs the finite dimensional uniserial KΓ/<ρ>-modules are unwindable.
Let Γ be an arrow unique graph with commutativity relations, ρ. In Section 2, the concept of unwindable modules is used to determine whether a certain factor ring of KΓ/<ρ> is of finite representation type.
In a different vein, the relationship between almost split sequences over Artin algebras and the almost split sequences over factor rings of such algebras is studied. Let Λ be an Artin algebra and let Λ̅ be a factor ring of Λ. Two sets of necessary and sufficient conditions are obtained for determining when an almost split sequence of Λ̅-modules remains an almost split sequence when viewed as a sequence of Λ-modules. / Ph. D.
|
8 |
Auslander-Reiten theory for systems of submodule embeddingsUnknown Date (has links)
In this dissertation, we will investigate aspects of Auslander-Reiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute Auslander-Reiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and Ringel-Tachikawa Theorem which states that for an artinian ring R of finite representation type, each R-module is a direct sum of finite-length indecomposable R-modules. In cases where this applies, the indecomposable objects obtained in the Auslander-Reiten quiver give the building blocks for the objects in the category. We also briefly discuss in which cases systems of submodule embeddings form a Frobenius category, and for a few examples explore pointwise Calabi-Yau dimension of such a category. / by Audrey Moore. / Thesis (Ph.D.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.
|
9 |
Complexidade de Módulos / Complexity of ModulesKameyama, Silvana 16 February 2012 (has links)
A complexidade de um módulo M, sobre uma álgebra de dimensão finita R, é a medida do crescimento da dimensão de suas sizigias. No nosso trabalho, estudamos esse conceito, nos concentrando muito mais no caso das álgebras autoinjetiva. Relacionamos esse crescimento com o comportamento da componente do carcás de Auslander-Reiten, a qual o módulo M pertence. Em particular, estudamos, com bastante cuidado, o caso em que a complexidade é 1, o que significa que a dimensão das sizigias são eventualmente constante. Surpreendentemente, o comportamento de todos os módulos numa mesma componente é muito parecido. / The complexity of a module M under a finite dimensional algebra R is the measure of the growth of its syzygies\' dimension. In our work, we study this concept concentrating on the case of the selfinjective algebras. We relate this growth with the behavior of the Auslander-Reiten component containing this module. In particular, we study, carefully, the case in which the complexity is 1. Surprisingly, the behavior of every module in the same component as M is very similar.
|
10 |
Complexidade de Módulos / Complexity of ModulesSilvana Kameyama 16 February 2012 (has links)
A complexidade de um módulo M, sobre uma álgebra de dimensão finita R, é a medida do crescimento da dimensão de suas sizigias. No nosso trabalho, estudamos esse conceito, nos concentrando muito mais no caso das álgebras autoinjetiva. Relacionamos esse crescimento com o comportamento da componente do carcás de Auslander-Reiten, a qual o módulo M pertence. Em particular, estudamos, com bastante cuidado, o caso em que a complexidade é 1, o que significa que a dimensão das sizigias são eventualmente constante. Surpreendentemente, o comportamento de todos os módulos numa mesma componente é muito parecido. / The complexity of a module M under a finite dimensional algebra R is the measure of the growth of its syzygies\' dimension. In our work, we study this concept concentrating on the case of the selfinjective algebras. We relate this growth with the behavior of the Auslander-Reiten component containing this module. In particular, we study, carefully, the case in which the complexity is 1. Surprisingly, the behavior of every module in the same component as M is very similar.
|
Page generated in 0.0468 seconds