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TMF, 1999, Volume 119, Number 3, Pages 381–396 (Mi tmf746)  

This article is cited in 6 scientific papers (total in 6 papers)

Measures on diffeomorphism groups for non-Archimedean manifolds: Group representations and their applications

S. V. Lyudkovskii

General Physics Institute named after A. M. Prokhorov, Russian Academy of Sciences

Abstract: Nondegenerate $\sigma$-additive measures with ranges in $\mathbb R$ and $\mathbb Q_q$ ($q\ne p$ are prime numbers) that are quasi-invariant and pseudodifferentiable with respect to dense subgroups $G'$ are constructed on diffeomorphism and homeomorphism groups $G$ for separable non-Archimedean Banach manifolds $M$ over a local field $\mathbb K$$\mathbb K\supset\mathbb Q_p$, where $\mathbb Q_p$ is the field of $p$-adic numbers. These measures and the associated irreducible representations are used in the non-Archimedean gravitation theory.

DOI: https://doi.org/10.4213/tmf746

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English version:
Theoretical and Mathematical Physics, 1999, 119:3, 698–711

Bibliographic databases:

Received: 18.06.1998
Revised: 10.02.1999

Citation: S. V. Lyudkovskii, “Measures on diffeomorphism groups for non-Archimedean manifolds: Group representations and their applications”, TMF, 119:3 (1999), 381–396; Theoret. and Math. Phys., 119:3 (1999), 698–711

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Lyudkovskii, “Izmerimost avtomorfizmov topologicheskikh grupp”, Matem. zametki, 68:1 (2000), 105–112  mathnet  crossref  mathscinet  zmath
    2. S. V. Lyudkovskii, “Topological group representations that are generated by Poisson measures”, Russian Math. Surveys, 56:1 (2001), 166–167  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. S. V. Lyudkovskii, “Quasi-invariant and pseudo-differentiable measures with values in non-Archimedean fields on a non-Archimedean Banach space”, J. Math. Sci., 128:6 (2005), 3428–3460  mathnet  crossref  mathscinet  zmath  elib  elib
    4. S. V. Lyudkovskii, “Structure of diffeomorphism groups of non-Archimedean manifolds”, Russian Math. Surveys, 58:6 (2003), 1204–1205  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Khrennikov A., Ludkovsky S., “Non-archimedean stochastic processes”, Ultrametric Functional Analysis, Contemporary Mathematics Series, 319, 2003, 139–157  crossref  mathscinet  zmath  isi
    6. S. V. Lyudkovskii, “Topological Transformation Groups of Manifolds over Non-Archimedean Fields, Their Representations, and Quasi-Invariant Measures, II”, Journal of Mathematical Sciences, 150:4 (2008), 2123–2223  mathnet  crossref  mathscinet  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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