Essays about: "Lie algebra"

Showing result 1 - 5 of 23 essays containing the words Lie algebra.

  1. 1. Examples of G-Hom-Associative Algebras

    University essay from Mälardalens universitet/Akademin för utbildning, kultur och kommunikation

    Author : Felicia Modin; [2024]
    Keywords : G-hom-associative algebra; hom-associative algebra; hom-Lie admissible algebra;

    Abstract : 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

  3. 2. Integrability of super spin chains in 6D N=(1,0) SCFTs

    University essay from Uppsala universitet/Teoretisk fysik

    Author : Zuxian He; [2023]
    Keywords : 6D SCFTs; integrability; spin chains; representation theory; symmetry; oscillators; Lie algebra;

    Abstract : Superconformal field theories (SCFTs) are an important class of quantum field theories. These SCFTs have been a significant component in exploring and comprehending the fundamental framework of quantum field theories. READ MORE

  4. 3. The Ext-Algebra of Standard Modules of Bound Twisted Double Incidence Algebras

    University essay from Uppsala universitet/Algebra, logik och representationsteori

    Author : Mika Norlén Jäderberg; [2023]
    Keywords : Algebras; Finite-dimensional; Partially ordered sets; Modules; Quasi-hereditary; Ext-algebra; Schur algebra; Quiver; Path algebra; Categories; Morita equivalence; Yoneda product; Standard module; Homological algebra; Cohomology; Anick Chains;

    Abstract : 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

  5. 4. On Lie groups, Algebra, and the construction of an exceptional Lie group

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Elias Berg; [2023]
    Keywords : ;

    Abstract : An overview of some concepts regarding Lie groups, Lie algebra, culminating in the construction of an exceptional Lie group .... READ MORE

  6. 5. Classification Of Finite-Dimensional Complex Semi-Simple Lie Algebras And Serre’s Theorem

    University essay from Uppsala universitet/Algebra, logik och representationsteori

    Author : Bim Gustavsson; [2022]
    Keywords : ;

    Abstract : 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