Automorphisms of Mn,partially ordered by the star order |
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Authors: | Peter Legisa |
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Affiliation: | Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia,Communicated by R. Loewy, |
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Abstract: | Let Mn be the space of all n × n matrices with coefficients in [image omitted] or [image omitted], where n ≥ 3. The star order on Mn is defined by [image omitted] iff [image omitted], where A* is the Hermitian adjoint (i.e., the conjugate transpose) of A. We characterize surjective mappings Φ on Mn such that [image omitted] iff [image omitted]. The tools we use are the Fundamental theorem of projective geometry, Wigner's theorem, and the Penrose decomposition, which we need to describe the main result as well. |
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Keywords: | Star partial order Poset Full matrix algebra Automorphism 2000 Mathematics Subject Classifications: 06A06 15A04 15A09 15A30 16S50 |
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