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

University of Udine
University of Birmingham

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

Abstract

Axial algebras of Monster type 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 (a, β) naturally split into three cases: the case when a\not \in {2β,4β}, the case a=4β and a=4β. 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	2023
Issue number	636
DOIs	https://doi.org/10.1016/j.jalgebra.2023.08.020
Publication status	Published - 2023

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Monster algebra
axial algebra

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10.1016/j.jalgebra.2023.08.020

Cite this

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

abstract = "Axial algebras of Monster type 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 (a, β) naturally split into three cases: the case when a\textbackslash{}not \textbackslash{}in \{2β,4β\}, the case a=4β and a=4β. In this paper we give a complete classification all 2-generated primitive axial algebras of Monster type (2β,β).",

keywords = "Monster algebra, axial algebra, Monster algebra, axial algebra",

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

year = "2023",

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

language = "English",

volume = "2023",

pages = "123--170",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "636",

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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

Y1 - 2023

N2 - Axial algebras of Monster type 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 (a, β) naturally split into three cases: the case when a\not \in {2β,4β}, the case a=4β and a=4β. 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 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 (a, β) naturally split into three cases: the case when a\not \in {2β,4β}, the case a=4β and a=4β. In this paper we give a complete classification all 2-generated primitive axial algebras of Monster type (2β,β).

KW - Monster algebra

KW - axial algebra

KW - Monster algebra

KW - axial algebra

UR - https://publicatt.unicatt.it/handle/10807/247814

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U2 - 10.1016/j.jalgebra.2023.08.020

DO - 10.1016/j.jalgebra.2023.08.020

M3 - Article

SN - 0021-8693

VL - 2023

SP - 123

EP - 170

JO - Journal of Algebra

JF - Journal of Algebra

IS - 636

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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