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On primitive axial algebras of Jordan type
by Jonathan I. Hall   Yoav Segev   Sergey Shpectorov

Vol. 13 No. 4 (2018) P.397~P.409
 DOI: https://doi.org/10.21915/BIMAS.2018403 10.21915/BIMAS.2018403

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 $\eta$ admit a Frobenius form, for any $\eta$.

KEYWORDS
Axial algebra, 3-transposition, Jordan algebra, Frobenius form

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 17A99; Secondary: 17C99, 17B69.

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