Split spin factor algebras

J. McInroy*, S. Shpectorov*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
15 Downloads (Pure)


Motivated by Yabe's classification of symmetric $2$-generated axial algebras of Monster type, we introduce a large class of algebras of Monster type $(\alpha, \frac{1}{2})$, generalising Yabe's $\mathrm{III}(\alpha,\frac{1}{2}, \delta)$ family. Our algebras bear a striking similarity with Jordan spin factor algebras with the difference being that we asymmetrically split the identity as a sum of two idempotents. We investigate the properties of this algebra, including the existence of a Frobenius form and ideals. In the $2$-generated case, where our algebra is isomorphic to one of Yabe's examples, we use our new viewpoint to identify the axet, that is, the closure of the two generating axes.
Original languageEnglish
Pages (from-to)380-397
Number of pages18
JournalJournal of Algebra
Early online date22 Dec 2021
Publication statusPublished - 1 Apr 2022

Bibliographical note

Funding Information:
The work of the second author has been supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation .

Publisher Copyright:
© 2021 Elsevier Inc.


  • Spin factor
  • Jordan algebra
  • Axial algebra
  • Monster type
  • 2-generated
  • Non-associative
  • Idempotent


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