Komutirajoče preslikave trikotnih algeber

diplomsko delo

Bojan Trebežnik (Author), Daniel Eremita (Mentor)

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

matematika;algebra;trikotna algebra;matrike;gnezdna algebra;preslikave;mutirajoča preslikava;bilinearne preslikave;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[B. Trebežnik]
UDC:	51(043.2)
COBISS:	18504712
Views:	2583
Downloads:	129
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Commuting maps of triangular algebras
Secondary 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 satis%es 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.
Secondary keywords:	Triangular algebra;upper triangular matrix algebra;nest algebra;commuting map;commuting trace of a bilinear map.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	49 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19360