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

Department of 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
Volume	13
Issue number	4
DOIs	https://doi.org/10.21915/BIMAS.2018403
State	Published - Dec 2018

Keywords

Axial algebra
3-transposition
Jordan algebra
Frobenius form

Access to Document

10.21915/BIMAS.2018403

Cite this

@article{c825cc66c82848e7a847ef8a21ddf6ea,

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.",

keywords = "Axial algebra, 3-transposition, Jordan algebra, Frobenius form",

author = "Hall, \{Jonathan I.\} and Yoav Segev and Sergey Shpectorov",

year = "2018",

month = dec,

doi = "10.21915/BIMAS.2018403",

language = "English",

volume = "13",

pages = "397--409",

journal = "Bulletin of the Institute of Mathematics",

issn = "2304-7895",

publisher = "Academia Sinica * Institute of Mathematics",

number = "4",

}

TY - JOUR

T1 - On primitive axial algebras of Jordan type

AU - Hall, Jonathan I.

AU - Segev, Yoav

AU - Shpectorov, Sergey

PY - 2018/12

Y1 - 2018/12

N2 - 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.

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

U2 - 10.21915/BIMAS.2018403

DO - 10.21915/BIMAS.2018403

M3 - Article

SN - 2304-7895

VL - 13

SP - 397

EP - 409

JO - Bulletin of the Institute of Mathematics

JF - Bulletin of the Institute of Mathematics

IS - 4

ER -

On primitive axial algebras of Jordan type

Abstract

Keywords

Access to Document

Fingerprint

Cite this