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Symmetry, Integrability and Geometry: Methods and Applications, 2014, Volume 10, 096, 20 pp.
DOI: https://doi.org/10.3842/SIGMA.2014.096 (Mi sigma961) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Invariant Poisson Realizations and the Averaging of Dirac Structures

José A. Vallejoa, Yurii Vorobievb

a Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, México
b Departamento de Matemáticas, Universidad de Sonora, México
Full-text PDF (445 kB) Citations (5)
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DOI: https://doi.org/10.3842/SIGMA.2014.096
Abstract: We describe an averaging procedure on a Dirac manifold, with respect to a class of compatible actions of a compact Lie group. Some averaging theorems on the existence of invariant realizations of Poisson structures around (singular) symplectic leaves are derived. We show that the construction of coupling Dirac structures (invariant with respect to locally Hamiltonian group actions) on a Poisson foliation is related with a special class of exact gauge transformations.
Keywords: Poisson structures; Dirac structures; geometric data; averaging operators.
Received: May 19, 2014; in final form September 9, 2014; Published online September 15, 2014
Bibliographic databases:
Document Type: Article
MSC: 53D17; 70G45; 53C12
Language: English
Citation: José A. Vallejo, Yurii Vorobiev, “Invariant Poisson Realizations and the Averaging of Dirac Structures”, SIGMA, 10 (2014), 096, 20 pp.
Citation in format AMSBIB
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\by Jos\'e~A.~Vallejo, Yurii~Vorobiev
\paper Invariant Poisson Realizations and the Averaging of Dirac Structures
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\yr 2014
\vol 10
\papernumber 096
\totalpages 20
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84907298186}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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    Full-text PDF :34
    References:28
     
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