On algebras generated by idempotents

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Abstract

Idempotents ($e^2=e$) in (nonassociative commutative) algebras (e.g., Jordan algebras) behave sometimes like involutions in a group. Indeed, in some (very) interesting cases one can associate an involutive automorphism of the algebra to an idempotent. This topic is related to Griess algebras (and the Monster group), Majorana algebras, Axial algebras (and the Fischer groups) and Miyamoto involutions. We explore mostly algebras generated by two idempotents, having in mind groups, and an extension of the results to algebras generated by finitely many idempotents (when possible). Joint work with Louis Rowen.Non UBCUnreviewedAuthor affiliation: Ben Gurion UniversityFacult
Original languageEnglish
Media of outputOnline
Size29 min
DOIs
StatePublished - 17 Nov 2016

Keywords

  • Mathematics
  • Group theory and generalizations
  • Topological groups, lie groups
  • Algebraic structures

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