Komutirajoče preslikave trikotnih algeber

Trebežnik, Bojan

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Title:	Komutirajoče preslikave trikotnih algeber
Authors:	ID Trebežnik, Bojan (Author) ID Eremita, Daniel (Mentor) More about this mentor...
Files:	UNI_Trebeznik_Bojan_2011.pdf (353,46 KB) MD5: 861FCBCAFD53D38B3FBF852357B042FD PID: 20.500.12556/dkum/e12c6ab5-257c-4e35-ab89-57a9042af29d
Language:	Slovenian
Work type:	Undergraduate thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V diplomskem delu deﬁniramo pojem trikotne algebre. Dokažemo nekatere osnovne lastnosti in podamo osnovne primere trikotnih algeber, med katerimi sta najpomembnejši algebra zgornje trikotnih matrik Tn(R) in gnezdna algebra T(N). V nadaljevanju se ukvarjamo s komutirajočimi preslikavami trikotnih algeber. Preslikava f algebre A je komutirajoča, če velja f(a)a = af(a) za vsak a ∈ A. Zanima nas oblika komutirajoče linearne preslikave trikotne algebre. Glavni cilj tretjega poglavja je poiskati tak razred trikotnih algeber, katerih vse komutirajoče linearne preslikave imajo standardno obliko. Proučujemo tudi komutirajočo sled poljubne bilinearne preslikave B : U × U → U trikotne algebre U. Zanima nas oblika preslikave x → B(x, x), ki zadošča pogoju B(x, x)x−xB(x, x) = 0 za vsak x ∈ U. Naš cilj je poiskati tak razred trikotnih algeber, katerih vse komutirajoče sledi bilinearnih preslikav imajo standardno obliko.
Keywords:	Trikotna algebra, algebra zgornje trikotnih matrik, gnezdna algebra, komutirajoča preslikava, komutirajoča sled bilinearne preslikave.
Place of publishing:	Maribor
Publisher:	[B. Trebežnik]
Year of publishing:	2011
PID:	20.500.12556/DKUM-18907
UDC:	51(043.2)
COBISS.SI-ID:	18504712
NUK URN:	URN:SI:UM:DK:MM2IROKV
Publication date in DKUM:	07.07.2011
Views:	3133
Downloads:	165
Metadata:
Categories:	FNM
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Secondary language

Language:	English
Title:	Commuting maps of triangular algebras
Abstract:	In the graduation thesis the notion of a triangular algebra is introduced. We derive some of their basic properties and present classical examples of triangular algebras, among which the upper triangular matrix algebra Tn(R) and nest algebra T(N) are the most important. We proceed to study commuting maps of triangular algebras. A map f of an algebra A is called a commuting map if f(a)a = af(a) for every a ∈ A. We consider the form of a commuting map of a triangular algebra. The main purpose of the third chapter is to identify a class of triangular algebras for which every commuting linear map is proper. We also study a commuting trace of an arbitrary bilinear map B : U × U → U on a triangular algebra U. We consider the form of a map x → B(x, x), which satisﬁes the condition B(x, x)x − xB(x, x) = 0 for every x ∈ U. Our main purpose is to identify a certain class of triangular algebras for which every commuting trace of a bilinear map is proper.
Keywords:	Triangular algebra, upper triangular matrix algebra, nest algebra, commuting map, commuting trace of a bilinear map.

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