On injective Jordan semi-triple maps of matrix algebras

Gorazd Lešnjak; Nung Sing Sze

doi:10.1016/j.laa.2005.10.015

On injective Jordan semi-triple maps of matrix algebras

Gorazd Lešnjak, Nung Sing Sze

Research output: Journal article publication › Journal article › Academic research › peer-review

10 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 language	English
Pages (from-to)	383-388
Number of pages	6
Journal	Linear Algebra and Its Applications
Volume	414
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2005.10.015
Publication status	Published - 1 Apr 2006
Externally published	Yes

Keywords

Field homomorphism
Map
Matrix algebra

ASJC Scopus subject areas

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

More information

10.1016/j.laa.2005.10.015

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AU - Sze, Nung Sing

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N2 - 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.

AB - 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.

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KW - Matrix algebra

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DO - 10.1016/j.laa.2005.10.015

M3 - Journal article

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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On injective Jordan semi-triple maps of matrix algebras

Abstract

Keywords

ASJC Scopus subject areas

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