Majorana representations of the symmetric group of degree 4.

DOI10.1016/j.jalgebra.2010.07.015zbMath1257.20011OpenAlexW1985123310WikidataQ56874357 ScholiaQ56874357MaRDI QIDQ618256

Sergey V. Shpectorov, Seress, Ákos, Alexander A. Ivanov, Dimitrii V. Pasechnik

Publication date: 14 January 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2010.07.015

zbMATH Keywords

Griess algebra\(2A\)-involutionsConway-Griess-Norton algebraMajorana representationsMonster group

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Simple groups: sporadic groups (20D08) Vertex operators; vertex operator algebras and related structures (17B69) Representations of sporadic groups (20C34)

Related Items (33)

Code algebras, axial algebras and VOAs ⋮ An infinite-dimensional 2-generated primitive axial algebra of monster type ⋮ Standard Majorana representations of the symmetric groups ⋮ An infinite family of axial algebras ⋮ Saturated Majorana representations of 𝐴₁₂ ⋮ Generalised dihedral subalgebras from the Monster ⋮ 2-generated axial algebras of Monster type (\(2 \beta,\beta\)) ⋮ On the classification of 2-generated axial algebras of Majorana type ⋮ Quotients of the Highwater algebra and its cover ⋮ Sectional nonassociativity of metrized algebras ⋮ From forbidden configurations to a classification of some axial algebras of Monster type ⋮ On Majorana representations of \(A _6\) and \(A _7\). ⋮ Majorana representations of \(A_5\). ⋮ Associative subalgebras of low-dimensional Majorana algebras ⋮ Universal axial algebras and a theorem of Sakuma ⋮ Majorana representation of the Monster group ⋮ Minimal 3-generated Majorana algebras ⋮ Enumerating 3-generated axial algebras of Monster type ⋮ Lattice-integrality of certain group-invariant integral forms in vertex operator algebras ⋮ Majorana algebras generated by a \(2A\) algebra and one further axis ⋮ Radicals of \(S_n\)-invariant positive semidefinite Hermitian forms ⋮ The Axes of a Majorana Representation of $$A_{12}$$ ⋮ An expansion algorithm for constructing axial algebras ⋮ Modules over axial algebras ⋮ Transposition Algebras ⋮ Classifying 2-generated symmetric axial algebras of Monster type ⋮ Closed Majorana representations of \(\{3, 4\}^+\)-transposition groups ⋮ Majorana algebra for the Hoffman-Singleton graph ⋮ Double axes and subalgebras of Monster type in Matsuo algebras ⋮ Primitive axial algebras of Jordan type ⋮ Majorana representation of A6 involving 3C-algebras ⋮ Griess algebras generated by the Griess algebras of two \(3A\)-algebras with a common axis ⋮ Weyl groups and vertex operator algebras generated by Ising vectors satisfying the (2B, 3C) condition

Uses Software

• GAP

Cites Work

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• A simple construction for the Fischer-Griess monster group
• Vertex operator algebras generated by two conformal vectors whose \(\tau\)-involutions generate \(S_{3}\).
• A new construction of the moonshine vertex operator algebra over the real number field
• Griess algebras and conformal vectors in vertex operator algebras
• 6-Transposition Property of  -Involutions of Vertex Operator Algebras

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