About: Normal forms of irreducible ${\germ{sl}}\sb 3$-valued zero curvature representations

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Description	One of the ways to overcome existing limitations of the famous Wahlquist-Estabrook procedure consists in employing normal forms of zero curvature representations (ZCR). While in case of $sl_{2}$ normal forms are known for a long time, the next step is made in this paper. We find normal forms of $sl_{3}$-valued ZCR that are not reducible to a proper subalgebra of $sl_{3}$. We also prove a reducibility theorem, which says that if one of the matrices in a ZCR (A, B) falls into a proper subalgebra of $sl_{3}$, then the second matrix either falls into the same subalgebra or the ZCR is in a sense trivial. In the end of this paper we show examples of ZCR and their normal forms. One of the ways to overcome existing limitations of the famous Wahlquist-Estabrook procedure consists in employing normal forms of zero curvature representations (ZCR). While in case of $sl_{2}$ normal forms are known for a long time, the next step is made in this paper. We find normal forms of $sl_{3}$-valued ZCR that are not reducible to a proper subalgebra of $sl_{3}$. We also prove a reducibility theorem, which says that if one of the matrices in a ZCR (A, B) falls into a proper subalgebra of $sl_{3}$, then the second matrix either falls into the same subalgebra or the ZCR is in a sense trivial. In the end of this paper we show examples of ZCR and their normal forms. (en) Jedna z možných cest k překonání existujících omezení známé Wahlquist-Estabrookovi procedůry spočívá v zavedení normálních tvarů reprezentací nulové křivosti (ZCR). Zatím co v případě $sl_{2}$ jsou normální tvary známy dlouho, další krok je proveden v téhle práci. Hledáme normální tvary ZCR s hodnotami v $sl_3$ které nejsou reducibilní na vlastní podalgebru algebry $sl_3$. Taky dokážeme teorém o reducibilitě, který tvrdí, že pokuď jedna z matic v ZCR (A, B) padne do vlastní podalgebry $sl_3$, pak buď druhá matice padne do téže podalgebry, nebo daná ZCR je v určitém smyslu triviální. Na konci téhle práce pak ukážeme některé příklady ZCR a jejích normálních tvarů. (cs)
Title	Normal forms of irreducible ${\germ{sl}}\sb 3$-valued zero curvature representations Normální tvary ireducibilních reprezentací nulové křivosti s hodnotami v algebře $sl_3$ (cs) Normal forms of irreducible ${\germ{sl}}\sb 3$-valued zero curvature representations (en)
skos:prefLabel	Normal forms of irreducible ${\germ{sl}}\sb 3$-valued zero curvature representations Normální tvary ireducibilních reprezentací nulové křivosti s hodnotami v algebře $sl_3$ (cs) Normal forms of irreducible ${\germ{sl}}\sb 3$-valued zero curvature representations (en)
skos:notation	RIV/47813059:19610/05:#0000041!RIV06-GA0-19610___
http://linked.open.../vavai/riv/strany	435;445
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/04/0538), Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2006
http://linked.open...aciTvurceVysledku	Sebestyén, Peter
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	533080
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/05:#0000041
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	zero curvature representation; gauge transformation; normal form; nonlinear partial differential equation; jet space (en)
http://linked.open.../riv/klicoveSlovo	jet space gauge transformation normal form zero curvature representation nonlinear partial differential equation
http://linked.open...odStatuVydavatele	PL - Polská republika
http://linked.open...ontrolniKodProRIV	[0E14AD9FB12F]
http://linked.open...i/riv/nazevZdroje	Reports on Mathematical Physics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Geometry of integrable systems
http://linked.open...UplatneniVysledku	2005
http://linked.open...v/svazekPeriodika	55
http://linked.open...iv/tvurceVysledku	Sebestyén, Peter
http://linked.open...n/vavai/riv/zamer	Topological and analytical methods in the theory of dynamical systems and mathematical physics
issn	0034-4877
number of pages	11 (xsd:int)
http://localhost/t...ganizacniJednotka	19610
is http://linked.open...avai/riv/vysledek of	Normal forms of irreducible ${\germ{sl}}\sb 3$-valued zero curvature representations

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