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C ∞(M) as a smooth envelope of its subalgebras

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Abstract

A smooth envelope of a topological algebra is introduced, and the following result is announced: the smooth envelope of a given subalgebra A in C ∞(M) coincides with C ∞(M) if and only if A has the same tangent bundle as M.

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References

  1. S. S. Akbarov, “The Gelfand transform as a C*-envelope,” Mat. Zametki, 94 (5), 777–779 (2013).

    Article  MathSciNet  Google Scholar 

  2. S. S. Akbarov, “Pontryagin duality in the theory of topological vector spaces and in topological algebra,” Journal of Mathematical Sciences, 113 (2), 179–349 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. S. Akbarov, “Holomorphic functions of exponential type and duality for Stein groups with algebraic connected component of identity,” Journal of Mathematical Sciences, 162 (4), 459–586 (2009), http://arxiv.org/abs/0806.3205.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. S. Akbarov, “Envelopes and imprints in categories,” http://arxiv.org/abs/1110.2013.

  5. S. S. Akbarov, “C ∞-envelopes of topological algebras,” http://arxiv.org/abs/1303.2424.

  6. A. Connes, Noncommutative Geometry (Academic Press, 1994).

    MATH  Google Scholar 

  7. M. Fragoulopoulou, “Spaces of representations and enveloping l.m.c. *-algebras,” Pacific J. Math. 95 (1), 61–73 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Ya Helemskii, Banach and Locally Convex Algebras (Clarendon Press. Oxford Mathematical Monographs, 1993).

    Google Scholar 

  9. A. Inoue, “Locally C*-algebra,” Mem. Fac. Sci. Kyushu Univ. Ser. A, 25 (2), 197–235 (1971).

    MATH  MathSciNet  Google Scholar 

  10. J. Kuznetsova, “A duality for Moore groups,” J. Oper. Theory, 69 (2), 101–130 (2013), http://arxiv.org/abs/0907.1409.

    MathSciNet  Google Scholar 

  11. A. Mallios, Topological Algebras (North Holland, Amsterdam, 1986).

    MATH  Google Scholar 

  12. G. J.Murphy, C*-Algebras and Operator Theory (Academic Press, Boston, 1990).

    Google Scholar 

  13. N. C. Phillips, “Inverse limits of C*-algebras,” J. Oper. Theory 19, 159–195 (1988).

    MATH  Google Scholar 

  14. A. Yu. Pirkovskii, “Arens-Michael envelopes, homological epimorphisms, and relatively quasi-free algebras,” Trudy Moskov.Mat. Obshch. 69, 34–125 (2008) [Trans. Moscow Math. Soc., 27–104 (2008)].

    MathSciNet  Google Scholar 

  15. J. L. Taylor, “Homology and cohomology for topological algebras,” Adv. Math. 9, 137–182 (1972).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Moscow Aviation Institute (National Research University), Moscow, Russia

    S. S. Akbarov

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  1. S. S. Akbarov
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Correspondence to S. S. Akbarov.

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The article was submitted by the author for the English version of the journal.

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Akbarov, S.S. C ∞(M) as a smooth envelope of its subalgebras. Math Notes 97, 489–492 (2015). https://doi.org/10.1134/S0001434615030207

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  • DOI: https://doi.org/10.1134/S0001434615030207

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