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

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Abstract

Nondegenerate σ-additive measures with ranges in ℝ and ℚq (q≠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 fieldK,K ⊃ ℚq, where ℚq is the field of p-adic numbers. These measures and the associated irreducible representations are used in the non-Archimedean gravitation theory.

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References

  1. C. J. Isham, “Topological and global aspects of quantum theory,” in:Relativity, Groups, and Topology: II (B. S. De Witt, ed.), North-Holland, Amsterdam (1984), p. 1059.

    Google Scholar 

  2. I. Ya. Aref'eva, B. Dragovich, P. H. Frampton, and I. V. Volovich,Int. J. Mod. Phys.,6, 4341 (1991).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov,p-Adic Analysis and Mathematical Physics [in Russian], Nauka, Moscow (1994); English transl. World Scientific, Singapore (1994).

    Google Scholar 

  4. A. C. M. van Rooij,Non-Archimedean Functional Analysis, Marcel Dekker, New York (1978).

    MATH  Google Scholar 

  5. S. V. Ludkovsky,Southeast Asian Bull. Math.,22, 301 (1998).

    MathSciNet  Google Scholar 

  6. S. V. Ludkovskii,Russ. Math. Surv.,51, 338 (1996).

    Article  Google Scholar 

  7. S. V. Ludkovskii,Russ. Math. Surv.,51, 559 (1996).

    Article  Google Scholar 

  8. S. V. Ludkovsky, “Representations and structure of groups of diffeomorphisms, of non-Archimedean Banach manifolds: I, II,” Preprint Nos. IC/96/180, 181, ICTP, Trieste (1996); http://www.ictp.trieste.it.

  9. E. T. Shavgulidze,Sov. Math. Dokl.,38, 622 (1989).

    MATH  MathSciNet  Google Scholar 

  10. W. H. Schikhof,Ultrametric Calculus, Cambridge Univ. Press, Cambridge (1984).

    MATH  Google Scholar 

  11. Yu. L. Dalecky and S. V. Fomin,Measures and Differential Equations in Infinite-Dimensional Space [in Russian], Nauka, Moscow (1978); English transl. Kluwer, Dordrecht (1991).

    Google Scholar 

  12. V. S. Vladimirov,Russ. Math. Surv.,43, 19 (1988).

    Article  MATH  Google Scholar 

  13. S. V. Ludkovsky, “Quasi-invariant and pseudodifferentiable measures on a non-Archimedean Banach space,” Preprint IC/96/210, ICTP, Trieste (1996); Deposited [in Russian] VINITI No. 3353-B97, 17.11.1997, VINITI, Moscow (1997).

  14. J. M. G. Fell and R. S. Doran,Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Acad. Press, Boston (1988).

    Google Scholar 

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Authors and Affiliations

  1. Institute for General Physics, RAS, Moscow, Russia

    S. V. Lyudkovskii

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  1. S. V. Lyudkovskii
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 3, pp. 381–396, June, 1999.

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Lyudkovskii, S.V. Measures on diffeomorphism groups for non-archimedean manifolds: Group representations and their applications. Theor Math Phys 119, 698–711 (1999). https://doi.org/10.1007/BF02557380

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  • DOI: https://doi.org/10.1007/BF02557380

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