On classical adjoint-commuting mappings between matrix algebras |
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Authors: | Wai Leong Chooi Wei Shean Ng |
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Institution: | a Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia b Department of Mathematical Sciences, Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia |
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Abstract: | Let F be a field and let m and n be integers with m,n?3. Let Mn denote the algebra of n×n matrices over F. In this note, we characterize mappings ψ:Mn→Mm that satisfy one of the following conditions:- 1.
- |F|=2 or |F|>n+1, and ψ(adj(A+αB))=adj(ψ(A)+αψ(B)) for all A,B∈Mn and α∈F with ψ(In)≠0.
- 2.
- ψ is surjective and ψ(adj(A-B))=adj(ψ(A)-ψ(B)) for every A,B∈Mn.
Here, adjA denotes the classical adjoint of the matrix A, and In is the identity matrix of order n. We give examples showing the indispensability of the assumption ψ(In)≠0 in our results. |
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Keywords: | 15A03 15A04 |
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