General preservers of quasi-commutativity

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Title:	General preservers of quasi-commutativity
Authors:	ID Dolinar, Gregor (Author) ID Kuzma, Bojan (Author)
Files:	http://dx.doi.org/10.4153/CJM-2010-041-x
Language:	English
Work type:	Not categorized
Typology:	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
PID:	20.500.12556/RUP-7732
ISSN:	0008-414X
UDC:	512.643
COBISS.SI-ID:	15627353
Publication date in RUP:	02.04.2017
Views:	2915
Downloads:	81
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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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