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Maps on idempotent matrices over division rings
Šemrl, Peter
Naj bo ▫$\mathbb{D}$▫ poljuben obseg (komutativen ali nekomutativen) in naj bo ▫$P_n(\mathbb{D})$▫ množica vseh ▫$n\times n$▫ idempotentnih matrik nad obsegom ▫$\mathbb{D}$▫. Ob privzetku nekaterih ...dokaj milih pogojev opišemo splošno obliko preslikav na ▫$P_n(\mathbb{D})$▫, ki ohranjajo komutativnost ali urejenost ali pravokotnost. S kontraprimeri pokažemo optimalnost dobljenih rezultatov. Dobljene rezultate uporabimo za dokaz kvaternionske verzije Ovchinnikovega rezultata, ki je pomemben v kvantni mehaniki. Uporabni so tudi pri študiju avtomorfizmov operatorskih in matričnih polgrup, lokalnih avtomorfizmov, linearnih ohranjevalcev in v geometriji matrik in Grassmannovih prostorov.
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