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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10104517" target="_blank" >RIV/00216208:11320/12:10104517 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/mma.1527" target="_blank" >http://dx.doi.org/10.1002/mma.1527</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mma.1527" target="_blank" >10.1002/mma.1527</a>

Result language
angličtina
Original language name
The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces
Original language 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-actionof 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 blocksare 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F08%2F0397" target="_blank" >GA201/08/0397: Algebraic methods in geometry and topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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