Three Families of Lie Algebras of Exponential Growth from Vertex Operator Algebras

2021/06/30 by Legros, Gabriel B.
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2106.16178

Abstract

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 V_L from an even lattice L and provide an algebraic description of the Lie algebra g_II_25,1 from the perspective of 24 different Niemeier lattices N via the decomposition II_25,1 = N ⊕ II_1,1 using the no-ghost theorem. For N=1 SVOAs we review the construction of the Fock space V_NS and provide an explicit basis for the spectrum-generating algebra of the Lie algebra g_NS. For N=2 SVOAs, we describe the structure of g⁽²⁾_NS explicitly as a ℚ-graded Lie algebra and we lift a left and right SL(2,ℤ) action on II_2,2 to g⁽²⁾_NS.

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