Semiassociative algebras over a field

Guy Blachar, Darrell Haile, Eliyahu Matzri, Edan Rein, Uzi Vishne

Research output: Contribution to journalArticlepeer-review

Abstract

An associative central simple algebra is a form of a matrix algebra, because a maximal étale subalgebra acts on the algebra faithfully by left and right multiplication. In an attempt to extract and isolate the full potential of this point of view, we study nonassociative algebras whose nucleus contains an étale subalgebra bi-acting faithfully on the algebra. These algebras, termed semiassociative, are shown to be the forms of skew matrix algebras, which we are led to define and investigate. Semiassociative algebras modulo skew matrix algebras compose a Brauer monoid, which contains the Brauer group of the field as a unique maximal subgroup.

Original languageEnglish
Pages (from-to)35-84
Number of pages50
JournalJournal of Algebra
Volume649
DOIs
StatePublished - 1 Jul 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

  • Brauer group
  • Central simple algebras
  • Deformation of matrix algebras
  • Maximal subfield
  • Nonassociative algebra

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