20.500.12556/DKUM-64561 Avtomorfizmi trikotnih matričnih algeber Automorphisms of triangular matrix algebras 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 tedaj, 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. 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). algebra zgornje trikotna matrična algebra avtomorfizem antiavtomorfizem jordanski avtomorfizem Liejev avtomorfizem. Algebra upper triangular matrix algebra automorphism antiautomorphism Jordan automorphism Lie automorphism. true true false [B. Lopert] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2016-10-23 18:43:23 2016-11-25 13:39:47 2022-07-05 03:08:19 2019-07-11 14:05:51 2016 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.55(043.2) 22788104 URN:SI:UM:DK:QNKIA7RI MAG_Lopert_Bogdan_2016.pdf MAG_Lopert_Bogdan_2016.pdf 1 BE40202A5761100777CEEB563269DABF 59cfb4c57a2925028ae398bd1b7944eb2992ebe928cca621cbae611a683ba486 d193692d-7c0d-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=107892 Fakulteta za naravoslovje in matematiko 0 0 0