Modular moonshine. II

DOI10.1215/S0012-7094-96-08315-5zbMath1032.17049OpenAlexW2072712334MaRDI QIDQ1918384

Richard E. Borcherds, Alexander J. E. Ryba

Publication date: 12 September 1999

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-96-08315-5

zbMATH Keywords

moonshine conjecturessporadic groupvanishing theorem for cohomologymonster simple groupHeld groupBrauer traces of \(p\)-regular elementscohomology and modular representationshauptmodulsmonster vertex algebravertex superalgebras mod \(p\)

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Modular representations and characters (20C20) Relationship to Lie algebras and finite simple groups (11F22) Vertex operators; vertex operator algebras and related structures (17B69) Representations of sporadic groups (20C34)

Related Items

Modular \(A_{n}(V)\) theory ⋮ Generalized Kac-Moody algebras and some related topics ⋮ Smash product construction of modular lattice vertex algebras ⋮ Moonshine ⋮ Modular Virasoro vertex algebras and affine vertex algebras ⋮ A self-dual integral form of the moonshine module ⋮ Transformations among large \(c\) conformal field theories ⋮ THE MOONSHINE MODULE FOR CONWAY’S GROUP ⋮ Generalized moonshine. II: Borcherds products ⋮ \(p\)-adic vertex operator algebras ⋮ On integral forms for vertex algebras associated with affine Lie algebras and lattices ⋮ Modular moonshine. III. ⋮ The fake monster formal group ⋮ The 5-modular characters of the sporadic simple Harada-Norton group \(HN\) and its automorphism group \(HN.2\). ⋮ Representations of vertex operator algebras over an arbitrary field ⋮ Vertex operator algebras associated to the Virasoro algebra over an arbitrary field ⋮ Symmetric invariant bilinear forms on modular vertex algebras ⋮ Integral forms in vertex operator algebras, a survey ⋮ Super-moonshine for Conway's largest sporadic group ⋮ Lattice structure of modular vertex algebras ⋮ A composite order generalization of modular moonshine ⋮ Integral structures in extended affine Lie algebras ⋮ Twisted modules for affine vertex algebras over fields of prime characteristic ⋮ A natural invariant algebra for the Baby Monster group ⋮ Intertwining operators among modules for affine Lie algebra and lattice vertex operator algebras which respect integral forms

Cites Work

• Characters and cohomology of finite groups
• A simple construction for the Fischer-Griess monster group
• Calculation of the 7-modular characters of the Held group
• Monstrous moonshine and monstrous Lie superalgebras
• Third and higher order NFPA twisted constructions of conformal field theories from lattices
• Theq—-series of monstrous moonshine & the decomposition of the head characters
• Vertex algebras, Kac-Moody algebras, and the Monster
• Monstrous Moonshine
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