magistrsko delo
Bogdan Lopert (Author), Dominik Benkovič (Mentor)

Abstract

V magistrskem delu so na algebri zgornje trikotnih matrik obravnavani in karakterizirani avtomorfizmi, jordanski izomorfizmi in Liejevi avtomorfizmi. V delu dokažemo,da je vsak avtomorfizem na algebri zgornje trikotnih matrik Tn(K), kjer je K komutativen kolobar z enoto, notranji. Vsak jordanski izomorfizem ki slika iz algebre Tn(K) v poljubno algebro A, je bodisi izomorfizem bodisi antiizomorfizem natanko takrta, ko je kolobar K povezan. Vsak Liejev avtomorfizem na algebri Tn(F), kjer je F polje, se lahko zapiše kot vsota avtomorfizma in linearne preslikave, ki slika v center algebre Tn(F) in uniči komutatorje ali pa kot vsota negativnega antiavtomorfizma in linearne preslikave, ki slika v center algebre Tn(F) in uniči komutatorje.

Keywords

magistrska dela;algebra;zgornje trikotna matrična algebra;avtomorfizem;antiavtomorfizem;jordanski avtomorfizem;Liejev avtomorfizem;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [B. Lopert]
UDC: 512.55(043.2)
COBISS: 22788104 Link will open in a new window
Views: 995
Downloads: 131
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: English
Secondary title: Automorphisms of triangular matrix algebras
Secondary abstract: In the master's thesis, automorphisms, Jordan isomorphisms and Lie automorphisms of the upper triangular matrix algebra are discussed and characterized. We prove that every automorphism on the upper triangular matrix algebra Tn(K), where K is a commutative ring with unity, is an inner automorphism. Each Jordan isomorphism, which maps from algebra Tn(K) into an algebra A, is either an isomorphism or an antiisomorphism precisely when the ring K is connected. Each Lie automorphism on algebra Tn(F), where F is a field, can be written as a sum of an automorphism and linear mapping which maps into the centre of algebra Tn(F) and vanishes on all commutators of algebra Tn(F) or a sum of an negative antiautomorphism and linear mapping which maps into the centre of algebra Tn(F) and vanishes on all commutators of algebra Tn(F).
Secondary keywords: master theses;algebra;upper triangular matrix algebra;automorphism;antiautomorphism;Jordan automorphism;Lie automorphism;
URN: URN:SI:UM:
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: 51 f.
ID: 9204086