Axes of Jordan type in non-commutative algebras

Louis Rowen, Yoav Segev

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The Peirce decomposition of a Jordan algebra with respect to an idempotent is well known. This decomposition was taken one step further and generalized recently by Hall, Rehren and Shpectorov, with their introduction of axial algebras, and in particular primitive axial algebras of Jordan type (PAJs for short). It turns out that these notions are closely related to three-transposition groups and vertex operator algebras. De Medts, Peacock, Shpectorov and M. Van Couwenberghe generalized axial algebras to decomposition algebras which, in particular, are not necessarily commutative. This paper deals with decomposition algebras which are non-commutative versions of PAJs.

Original languageEnglish
Article number2350094
JournalJournal of Algebra and its Applications
Volume22
Issue number4
DOIs
StatePublished - 1 Apr 2023

Bibliographical note

Publisher Copyright:
© 2023 World Scientific Publishing Company.

Keywords

  • Axis
  • flexible algebra
  • fusion rules
  • idempotent
  • power-associative

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