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TMF, 2003, Volume 135, Number 1, Pages 70–81 (Mi tmf171)  

This article is cited in 7 scientific papers (total in 7 papers)

Prolongations of Vector Fields on Lie Groups and Homogeneous Spaces

S. P. Baranovskii, I. V. Shirokov

Omsk State University

Abstract: We introduce the notion of the $\mathfrak{gl}(V)$-prolongation of Lie algebras of differential operators on homogeneous spaces. The $\mathfrak{gl}(V)$-prolongations are topological invariants that coincide with one-dimensional cohomologies of the corresponding Lie algebras in the case where $V$ is a homogeneous space. We apply the obtained results to the spaces $S^1$ (the Virasoro algebra) and $\mathbb R^1$.

Keywords: Lie groups, homogeneous spaces, vector fields, Lie algebra cohomologies

DOI: https://doi.org/10.4213/tmf171

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English version:
Theoretical and Mathematical Physics, 2003, 135:1, 510–519

Bibliographic databases:

Received: 01.04.2002

Citation: S. P. Baranovskii, I. V. Shirokov, “Prolongations of Vector Fields on Lie Groups and Homogeneous Spaces”, TMF, 135:1 (2003), 70–81; Theoret. and Math. Phys., 135:1 (2003), 510–519

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
\yr 2003
\vol 135
\issue 1
\pages 510--519
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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. Popovych, RO, “Realizations of real low-dimensional Lie algebras”, Journal of Physics A-Mathematical and General, 36:26 (2003), 7337  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. O. L. Kurnyavko, I. V. Shirokov, “Construction of invariant scalar particle wave equations on Riemannian manifolds with external gauge fields”, Theoret. and Math. Phys., 156:2 (2008), 1169–1179  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. S. P. Baranovskii, I. V. Shirokov, “Deformations of vector fields and canonical coordinates on coadjoint orbits”, Siberian Math. J., 50:4 (2009), 580–586  mathnet  crossref  mathscinet  isi  elib
    4. Breev A.I., Shapovalov A.V., “Yang-Mills Gauge Fields Conserving the Symmetry Algebra of the Dirac Equation in a Homogeneous Space”, XXII International Conference on Integrable Systems and Quantum Symmetries, Journal of Physics Conference Series, 563, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2014, 012004  crossref  mathscinet  isi  scopus  scopus
    5. 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
    6. Alexey A. Magazev, Vitaly V. Mikheyev, Igor V. Shirokov, “Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras”, SIGMA, 11 (2015), 066, 17 pp.  mathnet  crossref
    7. A. I. Breev, A. V. Shapovalov, “Polyarizatsiya vakuuma skalyarnogo polya na gruppakh Li s biinvariantnoi metrikoi”, Kompyuternye issledovaniya i modelirovanie, 7:5 (2015), 989–999  mathnet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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