On primitive axial algebras of Jordan type

Jonathan I. Hall; Yoav Segev; Sergey Shpectorov

On primitive axial algebras of Jordan type

Group Theory 2017-05-11 v1

Authors: Jonathan I. Hall , Yoav Segev , Sergey Shpectorov

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 algebras Jordan type primitive axial algebras 3-transposition groups Matsuo algebras Frobenius form

Cite

@article{arxiv.1705.03492,
  title  = {On primitive axial algebras of Jordan type},
  author = {Jonathan I. Hall and Yoav Segev and Sergey Shpectorov},
  journal= {arXiv preprint arXiv:1705.03492},
  year   = {2017}
}

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10 pages

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