Search for dissertations about: "linear algebra"

Showing result 1 - 5 of 82 swedish dissertations containing the words linear algebra.

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

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

    Abstract : 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. READ MORE

  4. 2. Simple Modules over Lie Algebras

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

    Abstract : 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. READ MORE

  5. 3. Around minimal Hilbert series problems for graded algebras

    Author : Lisa Nicklasson; Samuel Lundqvist; Christian Gottlieb; Uwe Nagel; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Graded algebras; Hilbert series; Lefschetz properties; Exterior algebra; Linear resolution; Mathematics; matematik;

    Abstract : The Hilbert series of a graded algebra is an invariant that encodes the dimension of the algebra's graded compontents. It can be seen as a tool for measuring the size of a graded algebra. This gives rise to the idea of algebras with a "minimal Hilbert series", among the algebras within a certain family. READ MORE

  6. 4. Around power ideals : From Fröberg's conjecture to zonotopal algebra

    Author : Gleb Nenashev; Boris Shapiro; Volkmar Welker; Stockholms universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Mathematics; matematik;

    Abstract : In this thesis we study power algebras, which are quotient of polynomial rings by power ideals. We will study Hilbert series of such ideals and their other properties. We consider two important special cases, namely, zonotopal ideals and generic ideals. Such ideals have a lot combinatorial properties. READ MORE

  7. 5. Ext-algebras of standard modules over quasi-hereditary algebras

    Author : Markus Thuresson; Julian Külshammer; Pierre-Guy Plamondon; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik;

    Abstract : This thesis concerns the representation theory of a particular class of finite-dimensional algebras, called quasi-hereditary algebras. In particular, it considers two subclasses of quasi-hereditary algebras: dual extension algebras and hereditary algebras. It consists of three papers. READ MORE