On primitive axial algebras of Jordan type

Jonathan I. Hall; Yoav Segev; Sergey Shpectorov

doi:10.21915/BIMAS.2018403

On primitive axial algebras of Jordan type

Jonathan I. Hall, Yoav Segev, Sergey Shpectorov

Mathematics

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

Abstract

In this note we give an overview of our knowledge regarding primitive axial algebras of Jordan type half and connections between 3-transposition groups and Matsuo algebras. We also show that primitive axial algebras of Jordan type η admit a Frobenius form, for any η.

Original language	English
Pages (from-to)	397-409
Number of pages	13
Journal	Bulletin of the Institute of Mathematics Academia Sinica New Series
Volume	13
Issue number	4
DOIs	https://doi.org/10.21915/BIMAS.2018403
Publication status	Published - 31 Dec 2018

Keywords

Axial algebra
3-transposition
Jordan algebra
Frobenius form

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title = "On primitive axial algebras of Jordan type",

abstract = "In this note we give an overview of our knowledge regarding primitive axial algebras of Jordan type half and connections between 3-transposition groups and Matsuo algebras. We also show that primitive axial algebras of Jordan type η admit a Frobenius form, for any η.",

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AU - Shpectorov, Sergey

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AB - In this note we give an overview of our knowledge regarding primitive axial algebras of Jordan type half and connections between 3-transposition groups and Matsuo algebras. We also show that primitive axial algebras of Jordan type η admit a Frobenius form, for any η.

KW - Axial algebra

KW - 3-transposition

KW - Jordan algebra

KW - Frobenius form

UR - https://arxiv.org/abs/1705.03492

U2 - 10.21915/BIMAS.2018403

DO - 10.21915/BIMAS.2018403

M3 - Article

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VL - 13

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JO - Bulletin of the Institute of Mathematics Academia Sinica New Series

JF - Bulletin of the Institute of Mathematics Academia Sinica New Series

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ER -

On primitive axial algebras of Jordan type

Abstract

Keywords

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