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:	03.04.2017
Views:	3401
Downloads:	85
Metadata:
:	DOLINAR, Gregor and KUZMA, Bojan, 2010, General preservers of quasi-commutativity. [online]. 2010. Vol. 62, no. 4, p. 758–786. [Accessed 5 April 2025]. Retrieved from: http://dx.doi.org/10.4153/CJM-2010-041-x Copy citation

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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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