Sökning: "Algebra och geometri"
Visar resultat 1 - 5 av 80 avhandlingar innehållade orden Algebra och geometri.
1. Waring-type problems for polynomials : Algebra meets Geometry
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
2. Morphisms of real calculi from a geometric and algebraic perspective
Sammanfattning : Noncommutative geometry has over the past four of decades grown into a rich field of study. Novel ideas and concepts are rapidly being developed, and a notable application of the theory outside of pure mathematics is quantum theory. LÄS MER
3. On the Clebsch-Gordan problem for quiver representations
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
4. Real and complex Monge-Ampère equations, statistical mechanics and canonical metrics
Sammanfattning : Recent decades has seen a strong trend in complex geometry to study canonical metrics and the way they relate to geometric analysis, algebraic geometry and probability theory. This thesis consists of four papers each contributing to this field. The first paper sets up a probabilistic framework for real Monge-Ampère equations on tori. LÄS MER
5. Classification of classical twists of the standard Lie bialgebra structure on a loop algebra
Sammanfattning : This licentiate thesis is based on the work "Classification of classical twists of the standard Lie bialgebra structure on a loop algebra" by R. Abedin and the author of this thesis. The standard Lie bialgebra structure on an affine Kac-Moody algebra induces a Lie bialgebra structure on the underlying loop algebra and its parabolic subalgebras. LÄS MER
