We study three families of infinite-dimensional Lie algebras defined from
Vertex Operator Algebras and their properties. For N=0 VOAs, we review the
construction of the Fock space VL from an even lattice L and provide an
algebraic description of the Lie algebra gII25,1 from the perspective
of 24 different Niemeier lattices N via the decomposition II25,1=N⊕II1,1 using the no-ghost theorem. For N=1 SVOAs we review the
construction of the Fock space VNS and provide an explicit basis for the
spectrum-generating algebra of the Lie algebra gNS. For N=2 SVOAs, we
describe the structure of gNS(2) explicitly as a Q-graded
Lie algebra and we lift a left and right SL(2,Z) action on
II2,2 to gNS(2).Comment: PhD dissertation, 2021, 152 page