Universal axial algebras and a theorem of Sakuma

DOI10.1016/j.jalgebra.2014.08.035zbMath1320.17015arXiv1311.0217OpenAlexW2081102812MaRDI QIDQ468713

Jonathan I. Hall, Sergey V. Shpectorov, Felix Rehren

Publication date: 7 November 2014

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

Full work available at URL: https://arxiv.org/abs/1311.0217

zbMATH Keywords

idempotentsfusion rulesmonster groupaxial algebrasnonassociative commutative algebras generated by axesuniversal Frobenius axial algebra

Mathematics Subject Classification ID

Structure theory for nonassociative algebras (17A60) Vertex operators; vertex operator algebras and related structures (17B69)

Related Items (34)

Non-associative Frobenius algebras for simply laced Chevalley groups ⋮ Code algebras, axial algebras and VOAs ⋮ An infinite-dimensional 2-generated primitive axial algebra of monster type ⋮ Killing metrized commutative nonassociative algebras associated with Steiner triple systems ⋮ An infinite family of axial algebras ⋮ Decomposition algebras and 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 ⋮ On primitive 3-generated axial algebras of Jordan type ⋮ Associative and Jordan algebras generated by two idempotents ⋮ Primitive 4-generated axial algebras of Jordan type ⋮ Miyamoto involutions in axial algebras of Jordan type half ⋮ From forbidden configurations to a classification of some axial algebras of Monster type ⋮ The universality of one half in commutative nonassociative algebras with identities ⋮ Majorana representation of the Monster group ⋮ Enumerating 3-generated axial algebras of Monster type ⋮ Miyamoto groups of code algebras ⋮ On an extremal property of Jordan algebras of Clifford type ⋮ A new series of axial algebras of monster type \((2\eta,\eta)\) ⋮ A characterization of algebras generated by idempotents ⋮ An expansion algorithm for constructing axial algebras ⋮ Research topics in finite groups and vertex algebras ⋮ On the structure of axial algebras ⋮ Modules over axial algebras ⋮ Transposition Algebras ⋮ Split spin factor algebras ⋮ Classifying 2-generated symmetric axial algebras of Monster type ⋮ Primitive axial algebras are of Jordan type ⋮ Code algebras which are axial algebras and their \(\mathbb{Z}_2\)-gradings ⋮ Double axes and subalgebras of Monster type in Matsuo algebras ⋮ Primitive axial algebras of Jordan type ⋮ The commutative nonassociative algebra of metric curvature tensors

Uses Software

• GAP

Cites Work

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• Majorana representations of the symmetric group of degree 4.
• A simple construction for the Fischer-Griess monster group
• The friendly giant
• Vertex operator algebras generated by two conformal vectors whose \(\tau\)-involutions generate \(S_{3}\).
• Griess algebras and conformal vectors in vertex operator algebras
• Primitive axial algebras of Jordan type
• Vertex algebras, Kac-Moody algebras, and the Monster
• 6-Transposition Property of  -Involutions of Vertex Operator Algebras

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