On injective Jordan semi-triple maps of matrix algebras

Gorazd Lešnjak, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)

Abstract

We show that every injective Jordan semi-triple map on the algebra Mn(F) of all n × n matrices with entries in a field F (i.e. a map Φ:Mn(F)→Mn(F) satisfyingΦ(ABA)=Φ(A)Φ(B)Φ(A)for every A and B in Mn(F)) is given by a map of the following form: there exist σ∈F, σ = ±1, an injective homomorphism φ of F and an invertible T∈Mn(F) such that eitherΦ(A)=σT- 1AφTforallA∈Mn(F),orΦ(A)=σT-1AφtTforallA∈Mn(F).Here, Aφ is the image of A under φ applied entrywise.
Original languageEnglish
Pages (from-to)383-388
Number of pages6
JournalLinear Algebra and Its Applications
Volume414
Issue number1
DOIs
Publication statusPublished - 1 Apr 2006
Externally publishedYes

Keywords

  • Field homomorphism
  • Map
  • Matrix algebra

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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