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Title: Generalized root graded Lie algebras
Author: Yaseen, Hogar M.
ISNI:       0000 0004 7428 3138
Awarding Body: University of Leicester
Current Institution: University of Leicester
Date of Award: 2018
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Let g be a non-zero finite-dimensional split semisimple Lie algebra with root system Δ. Let Γ be a finite set of integral weights of g containing Δ and {0}. We say that a Lie algebra L over F is generalized root graded, or more exactly (Γ,g)-graded, if L contains a semisimple subalgebra isomorphic to g, the g-module L is the direct sum of its weight subspaces Lα (α ∈ Γ) and L is generated by all Lα with α ̸= 0 as a Lie algebra. If g is the split simple Lie algebra and Γ = Δ∪{0} then L is said to be root-graded. Let g∼= sln and Θn = {0,±εi±ε j,±εi,±2εi | 1 ≤ i ̸= j ≤ n} where {ε1, . . . , εn} is the set of weights of the natural sln-module. Then a Lie algebra L is (Θn,g)-graded if and only if L is generated by g as an ideal and the g-module L decomposes into copies of the adjoint module, the natural module V, its symmetric and exterior squares S2V and ∧2V, their duals and the one dimensional trivial g-module. In this thesis we study properties of generalized root graded Lie algebras and focus our attention on (Θn, sln)-graded Lie algebras. We describe the multiplicative structures and the coordinate algebras of (Θn, sln)-graded Lie algebras, classify these Lie algebras and determine their central extensions.
Supervisor: Baranov, Alexander Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available