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Title:General preservers of quasi-commutativity
Authors:Kuzma, Bojan (Author)
Dolinar, Gregor (Author)
Files:URL http://dx.doi.org/10.4153/CJM-2010-041-x
 
Language:English
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:Let ▫$M_n$▫ be the algebra of all ▫$n \times n$▫ matrices over ▫$\mathbb{C}$▫. We say that ▫$A, B \in M_n$▫ quasi-commute if there exists a nonzero ▫$\xi \in \mathbb{C}$▫ such that ▫$AB = \xi BA$▫. In the paper we classify bijective not necessarily linear maps ▫$\Phi \colon M_n \to M_n$▫ which preserve quasi-commutativity in both directions.
Keywords:mathematics, linear algebra, general preserver, matrix algebra, quasi-commutativity
Year of publishing:2010
Number of pages:str. 758-786
Numbering:Vol. 62, no. 4
ISSN:0008-414X
UDC:512.643
COBISS_ID:15627353 Link is opened in a new window
Views:547
Downloads:43
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Secondary language

Language:Slovenian
Title:Splošni ohranjevalci kvazi-komutativnosti
Abstract:Naj bo ▫$M_n$▫ algebra vseh ▫$n \times n$▫ matrik nad obsegom ▫$\mathbb{C}$▫. Pravimo, da matriki ▫$A, B \in M_n$▫ kvazi-komutirata, če obstaja tak neničelni skalar ▫$\xi \in \mathbb{C}$▫, da je ▫$AB = \xi BA$▫. V članku klasificiramo bijektivne ne nujno linearne preslikave iz ▫$M_n$▫ v ▫$M_n$▫, ki ohranjajo kvazi-komutativnost v obeh smereh.
Keywords:matematika, linearna algebra, splošni ohranjevalci, matrična algebra, kvazi-komutativnost

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