Sökning: "Algebra och geometri"

Visar resultat 1 - 5 av 54 avhandlingar innehållade orden Algebra och geometri.

  1. 1. On the Clebsch-Gordan problem for quiver representations

    Författare :Martin Herschend; Ernst Dieterich; Alex Martsinkovsky; Karin Erdmann; Uppsala universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Algebra and geometry; quiver; quiver representation; tensor product; Clebsch-Gordan problem; representation ring; bialgebra; Galois covering; Algebra och geometri;

    Sammanfattning : On the category of representations of a given quiver we define a tensor product point-wise and arrow-wise. The corresponding Clebsch-Gordan problem of how the tensor product of indecomposable representations decomposes into a direct sum of indecomposable representations is the topic of this thesis. LÄS MER

  2. 2. Admissible transformations and the group classification of Schrödinger equations

    Författare :Celestin Kurujyibwami; Peter Basarab-Horwath; Roman Popovych; Pontelis Damianou; Linköpings universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES;

    Sammanfattning : We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. LÄS MER

  3. 3. N-complexes and Categorification

    Författare :Djalal Mirmohades; Volodymyr Mazorchuk; Steffen Oppermann; Uppsala universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Homological algebra; Category theory; Triangulated categories; K-theory; Hopfological algebra; Mathematics; Matematik;

    Sammanfattning : This thesis consists of three papers about N-complexes and their uses in categorification. N-complexes are generalizations of chain complexes having a differential d satisfying dN = 0 rather than d2 = 0. Categorification is the process of finding a higher category analog of a given mathematical structure. LÄS MER

  4. 4. Constructions of n-cluster tilting subcategories using representation-directed algebras

    Författare :Laertis Vaso; Martin Herschend; Øyvind Solberg; Uppsala universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURVETENSKAP; NATURAL SCIENCES; Representation theory; n-cluster tilting subcategory; Auslander–Reiten theory; representation-directed algebra; Nakayama algebra; global dimension; Mathematics; Matematik;

    Sammanfattning : One of the most useful tools in representation theory of algebras is Auslander–Reiten theory. A higher dimensional analogue has recently appeared, based on the notion of n-cluster tilting subcategories. LÄS MER

  5. 5. Simple Modules over Lie Algebras

    Författare :Jonathan Nilsson; Volodymyr Mazorchuk; Erhard Neher; Uppsala universitet; []
    Nyckelord :NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; Lie algebra; Representation; Simple module; Non-weight module; Classification; Construction; Mathematics; Matematik;

    Sammanfattning : Simple modules are the elemental components in representation theory for Lie algebras, and numerous mathematicians have worked on their construction and classification over the last century. This thesis consists of an introduction together with four research articles on the subject of simple Lie algebra modules. LÄS MER