Essays about: "Finite-dimensional"
Showing result 1 - 5 of 16 essays containing the word Finite-dimensional.
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1. The Ext-Algebra of Standard Modules of Bound Twisted Double Incidence Algebras
University essay from Uppsala universitet/Algebra, logik och representationsteoriAbstract : Quasi-hereditary algebras are an important class of algebras with many appli-cations in representation theory, most notably the representation theory of semi-simple complex Lie-algebras. Such algebras sometimes admit an exact Borel sub-algebra, that is a subalgebra satisfying similar formal properties to the Borel sub-algebras from Lie theory. READ MORE
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2. Determinantal Point Processes
University essay from KTH/FysikAbstract : We present and prove some important theorems regarding determinantal point processes. In particular we focus on existance and uniqueness theorems. Furthermore, we present an algorithm for generating determinantal point processes with a finite-dimensional projection kernel. READ MORE
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3. Classification Of Finite-Dimensional Complex Semi-Simple Lie Algebras And Serre’s Theorem
University essay from Uppsala universitet/Algebra, logik och representationsteoriAbstract : We consider finite-dimensional complex semi-simple Lie algebras g. Any such Lie algebra has a Cartan subalgebra h, and its adjoint representation on g yields a root space decomposition of g, which in turn gives rise to a root system. These are in turn classified by the Dynkin diagrams. READ MORE
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4. On Levi Decompositions in Finite and Infinite Dimensional Lie Algebras
University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)Abstract : In this bachelor thesis we introduce Lie algebras, and use Lie algebra cohomology to prove Levi's theorem about splitting of finite dimensional Lie algebras. We then construct the Virasoro algebra, compute its low dimensional cohomology spaces, and use this to demonstrate why Levi's theorem does not hold in the infinite dimensional case... READ MORE
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5. Finite-dimensional PT-symmetric Hamiltonians with an application to neutrino oscillations
University essay from KTH/Skolan för teknikvetenskap (SCI)Abstract : In this report, we first briefly summarize Hermitian quantum mechanics before moving on to the non-Hermitian case. We then review PT-symmetric quantum mechanics with a focus on finite-dimensional systems, and include a novel generalization of a perturbative calculation of the C-operator. READ MORE
