Essays about: "Lie algebras"
Showing result 1 - 5 of 19 essays containing the words Lie algebras.
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1. Examples of G-Hom-Associative Algebras
University essay from Mälardalens universitet/Akademin för utbildning, kultur och kommunikationAbstract : In this thesis we look at hom-associative algebras (which turn out to be exactly the G1-hom-associative algebras), by, in two and three dimensions, trying to find the structure constants for which an algebra becomes hom-associative when the homomorphism 𝛼 is defined as different matrix units. These algebras are also hom-Lie admissible (or G6-hom-associative, which turn out to be the same thing) with a commutator, so we also find the commutator for each of these hom-Lie admissible algebras. READ MORE
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2. 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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3. Spin Representations, Clifford Algebras and Spinors
University essay from Uppsala universitet/Matematiska institutionenAbstract : We begin by giving some theoretical background to the underlying concepts of spin representations and spinors. This is done from the perspective of Lie groups and Lie algebras. In particular, we discuss the functionality of Clifford algebras in the determination of the double-covering spin groups. READ MORE
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4. 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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5. 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
