A short introduction to the algebra, geometry, number theory and physics of moonshine

DOI10.1007/978-3-030-42400-8_1zbMath1454.81184OpenAlexW3041666503MaRDI QIDQ827157

John F. R. Duncan

Publication date: 7 January 2021

Full work available at URL: https://doi.org/10.1007/978-3-030-42400-8_1

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Relationship to Lie algebras and finite simple groups (11F22) Vertex operators; vertex operator algebras and related structures (17B69) Elliptic curves (14H52) Elliptic genera (58J26) Moduli, classification: analytic theory; relations with modular forms (14J15) Topology and geometry of orbifolds (57R18)

Related Items (1)

Class numbers, cyclic simple groups, and arithmetic

Cites Work

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• Lectures on Chevalley Groups
• Generalised Moonshine and Holomorphic Orbifolds
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• Lectures on K3 Surfaces
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• Uniqueness results for the moonshine vertex operator algebra
• Groups of Lie Type, Vertex Algebras, and Modular Moonshine
• THE MODULI SPACE OF N = 2 SUPER-RIEMANN SPHERES WITH TUBES
• Axiomatic Aspects ofN = 2 Vertex Superalgebras with Odd Formal Variables
• Supersymmetry of the Chiral de Rham Complex 2: Commuting Sectors
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• The Finite Simple Groups
• Arithmetic groups and the affine E8 Dynkin diagram
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• Gauss’ class number problem for imaginary quadratic fields
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• Monstrous Moonshine
• Finite Groups and Modular Functions
• Some Numerology between the Fischer-Griess Monster and the Elliptic Modular Function
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• A Simple Subgroup of M ? and E ₈ (3)
• Some Evidence for the Existence of a New Simple Group
• Solving elliptic diophantine equations: the general cubic case
• The Notion of N=1 Supergeometric Vertex Operator Superalgebra and the Isomorphism Theorem
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• A rigid local system with monodromy group the big Conway group $2.\mathsf {Co}_1$ and two others with monodromy group the Suzuki group $6.{{Suz}}$
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• Classification of holomorphic framed vertex operator algebras of central charge 24
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• Weight one Jacobi forms and umbral moonshine
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• Notes on Sphere Packings
• A Group of Order 8,315,553,613,086,720,000
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• The Fourier Series and the Functional Equation of the Absolute Modular Invariant J(τ)
• Divisibility Properties of the Fourier Coefficients of the Modular Invariant j(τ)
• Further Congruence Properties of the Fourier Coefficients of the Modular Invariant j(τ)
• Quasi Hopf algebras, group cohomology and orbifold models
• A hiker's guide to \(K3\). Aspects of \(N=(4,4)\) superconformal field theory with central charge \(c=6\)
• Modular-invariance of trace functions in orbifold theory and generalized Moonshine.

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