2-generated axial algebras of Monster type (2β,β)

Clara Franchi; Mario Mainardis; Sergey Shpectorov

doi:10.1016/j.jalgebra.2023.08.020

2-generated axial algebras of Monster type (2β,β)

Clara Franchi
, Mario Mainardis^*
, Sergey Shpectorov

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

Axial algebras of Monster type (α,β) are a class of non-associative algebras that includes, besides associative algebras, other important examples such as the Jordan algebras and the Griess algebra. 2-generated primitive axial algebras of Monster type (α,β) naturally split into three cases: the case when α∉{2β,4β}, the case α=4β and α=2β. In this paper we give a complete classification all 2-generated primitive axial algebras of Monster type (2β,β).

Original language	English
Pages (from-to)	123-170
Number of pages	48
Journal	Journal of Algebra
Volume	636
Early online date	30 Aug 2023
DOIs	https://doi.org/10.1016/j.jalgebra.2023.08.020
Publication status	Published - 15 Dec 2023

Bibliographical note

Funding Information:
We would like to thank the anonymous referee for the careful reading and precious comments.

Publisher Copyright:
© 2023 The Author(s)

Keywords

Axial algebras
Finite simple groups
Griess algebra
Matsuo algebras
Monster group

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2023.08.020Licence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

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title = "2-generated axial algebras of Monster type (2β,β)",

abstract = "Axial algebras of Monster type (α,β) are a class of non-associative algebras that includes, besides associative algebras, other important examples such as the Jordan algebras and the Griess algebra. 2-generated primitive axial algebras of Monster type (α,β) naturally split into three cases: the case when α∉\{2β,4β\}, the case α=4β and α=2β. In this paper we give a complete classification all 2-generated primitive axial algebras of Monster type (2β,β).",

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author = "Clara Franchi and Mario Mainardis and Sergey Shpectorov",

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doi = "10.1016/j.jalgebra.2023.08.020",

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T1 - 2-generated axial algebras of Monster type (2β,β)

AU - Franchi, Clara

AU - Mainardis, Mario

AU - Shpectorov, Sergey

PY - 2023/12/15

Y1 - 2023/12/15

N2 - Axial algebras of Monster type (α,β) are a class of non-associative algebras that includes, besides associative algebras, other important examples such as the Jordan algebras and the Griess algebra. 2-generated primitive axial algebras of Monster type (α,β) naturally split into three cases: the case when α∉{2β,4β}, the case α=4β and α=2β. In this paper we give a complete classification all 2-generated primitive axial algebras of Monster type (2β,β).

AB - Axial algebras of Monster type (α,β) are a class of non-associative algebras that includes, besides associative algebras, other important examples such as the Jordan algebras and the Griess algebra. 2-generated primitive axial algebras of Monster type (α,β) naturally split into three cases: the case when α∉{2β,4β}, the case α=4β and α=2β. In this paper we give a complete classification all 2-generated primitive axial algebras of Monster type (2β,β).

KW - Axial algebras

KW - Finite simple groups

KW - Griess algebra

KW - Matsuo algebras

KW - Monster group

UR - https://www.scopus.com/pages/publications/85172297858

U2 - 10.1016/j.jalgebra.2023.08.020

DO - 10.1016/j.jalgebra.2023.08.020

M3 - Article

AN - SCOPUS:85172297858

SN - 0021-8693

VL - 636

SP - 123

EP - 170

JO - Journal of Algebra

JF - Journal of Algebra

ER -

2-generated axial algebras of Monster type (2β,β)

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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