About: The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces

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Description	The classical Fischer decomposition of spinor-valued polynomials is a key result on solutions of the Dirac equation in the Euclidean space R^m. As is well-known, it can be understood as an irreducible decomposition with respect to the so-called L-action of the Pin group Pin(m). But, on Clifford algebra valued polynomials, we can consider also the H-action of Pin(m). In this paper, the corresponding Fischer decomposition for the H-action is obtained. It turns out that, in this case, basic building blocks are the spaces of homogeneous solutions to the Hodge-de Rham system. Moreover, it is shown that the Fischer decomposition for the H-action can be viewed even as a refinement of the classical one. The classical Fischer decomposition of spinor-valued polynomials is a key result on solutions of the Dirac equation in the Euclidean space R^m. As is well-known, it can be understood as an irreducible decomposition with respect to the so-called L-action of the Pin group Pin(m). But, on Clifford algebra valued polynomials, we can consider also the H-action of Pin(m). In this paper, the corresponding Fischer decomposition for the H-action is obtained. It turns out that, in this case, basic building blocks are the spaces of homogeneous solutions to the Hodge-de Rham system. Moreover, it is shown that the Fischer decomposition for the H-action can be viewed even as a refinement of the classical one. (en)
Title	The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces (en)
skos:prefLabel	The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces (en)
skos:notation	RIV/00216208:11320/12:10104517!RIV13-GA0-11320___
http://linked.open...avai/predkladatel	Matematicko-fyzikální fakulta
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/08/0397), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Lávička, Roman Souček, Vladimír
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	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	136711
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/12:10104517
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Hodge-de Rham systems; Fischer decomposition (en)
http://linked.open.../riv/klicoveSlovo	Fischer decomposition Hodge-de Rham systems
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[79B09490BB7C]
http://linked.open...i/riv/nazevZdroje	Mathematical Methods in the Applied Sciences
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Algebraic methods in geometry and topology
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	35
http://linked.open...iv/tvurceVysledku	Lávička, Roman Souček, Vladimír Delanghe, Richard
http://linked.open...ain/vavai/riv/wos	000298601900002
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	0170-4214
number of pages	7 (xsd:int)
http://bibframe.org/vocab/doi	10.1002/mma.1527
http://localhost/t...ganizacniJednotka	11320
is http://linked.open...avai/riv/vysledek of	The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces

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