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TMF, 2001, Volume 126, Number 3, Pages 393–408 (Mi tmf437)  

This article is cited in 10 scientific papers (total in 10 papers)

Identities and Invariant Operators on Homogeneous Spaces

I. V. Shirokov

Omsk State University

Abstract: We study identities (functional relations between the generators of the transformation group) and also algebras of invariant operators on homogeneous spaces using the method of orbits of the coadjoint representation (coadjoint orbits). This method permits establishing the relation between these two objects and elaborating an algorithm for their construction. A classification of homogeneous spaces is introduced based on the coadjoint orbit method.

DOI: https://doi.org/10.4213/tmf437

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English version:
Theoretical and Mathematical Physics, 2001, 126:3, 326–338

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Received: 24.08.2000

Citation: I. V. Shirokov, “Identities and Invariant Operators on Homogeneous Spaces”, TMF, 126:3 (2001), 393–408; Theoret. and Math. Phys., 126:3 (2001), 326–338

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. P. Baranovskii, I. V. Shirokov, “Prolongations of Vector Fields on Lie Groups and Homogeneous Spaces”, Theoret. and Math. Phys., 135:1 (2003), 510–519  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. A. Magazev, I. V. Shirokov, “Integration of Geodesic Flows on Homogeneous Spaces: The Case of a Wild Lie Group”, Theoret. and Math. Phys., 136:3 (2003), 1212–1224  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. A. Magazev, I. V. Shirokov, “Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces”, Russian Math. (Iz. VUZ), 50:8 (2006), 38–49  mathnet  mathscinet  elib
    4. I. V. Shirokov, “Differential invariants of the transformation group of a homogeneous space”, Siberian Math. J., 48:6 (2007), 1127–1140  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Goncharovskii M.M., Shirokov I.V., “Classification of Degenerate Solutions of Linear Differential Equations”, Russian Physics Journal, 54:5 (2011), 527–535  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    6. Breev A.I. Goncharovskii M.M. Shirokov I.V., “Klein-Gordon Equation with a Special Type of Nonlocal Nonlinearity in Commutative Homogeneous Spaces with Invariant Metric”, Russ. Phys. J., 56:7 (2013), 731–739  crossref  mathscinet  isi  scopus  scopus
    7. A. I. Breev, “Scalar field vacuum polarization on homogeneous spaces with an invariant metric”, Theoret. and Math. Phys., 178:1 (2014), 59–75  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Breev A.I., “Schrodinger Equation With Convolution Nonlinearity on Lie Groups and Commutative Homogeneous Spaces”, Russ. Phys. J., 57:8 (2014), 1050–1058  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Magazev A.A., “Magnetic Geodesic Flows on Homogeneous Manifolds”, Russ. Phys. J., 57:3 (2014), 312–320  crossref  zmath  isi  scopus  scopus
    10. M. M. Goncharovskiy, I. V. Shirokov, “Differential invariants and operators of invariant differentiation of the projectable action of Lie groups”, Theoret. and Math. Phys., 183:2 (2015), 619–636  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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