Sökning: "ALGEBRA"

Visar resultat 1 - 5 av 368 avhandlingar innehållade ordet ALGEBRA.

  1. 1. Waring-type problems for polynomials : Algebra meets Geometry

    Författare :Alessandro Oneto; Boris Shapiro; Brian Harbourne; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; polynomials; Waring problems; Hilbert series; fat points; power ideals; secant varieties; Mathematics; matematik;

    Sammanfattning : In the present thesis we analyze different types of additive decompositions of homogeneous polynomials. These problems are usually called Waring-type problems and their story go back to the mid-19th century and, recently, they received the attention of a large community of mathematicians and engineers due to several applications. LÄS MER

  3. 2. N-complexes and Categorification

    Författare :Djalal Mirmohades; Volodymyr Mazorchuk; Steffen Oppermann; Uppsala universitet; []
    Nyckelord :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. 3. Constructions of n-cluster tilting subcategories using representation-directed algebras

    Författare :Laertis Vaso; Martin Herschend; Øyvind Solberg; Uppsala universitet; []
    Nyckelord :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. 4. Stratified algebras and classification of tilting modules

    Författare :Elin Persson Westin; Volodymyr Mazorchuk; Aslak Buan; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Representation theory; Generalized tilting module; Exceptional sequence; Quasi-hereditary algebra; Standardly stratified algebra; Essential order; Category O; S-subcategory; Projective dimension; Finitistic dimension; Mathematics; Matematik;

    Sammanfattning : This thesis contains three papers in representation theory of algebras. It mainly studies two types of algebras; quasi-hereditary algebras and standardly stratified algebras. LÄS MER

  7. 5. Simple Modules over Lie Algebras

    Författare :Jonathan Nilsson; Volodymyr Mazorchuk; Erhard Neher; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; 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