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Mat. Sb. (N.S.), 1983, Volume 120(162), Number 4, Pages 528–539 (Mi msb2145)  

This article is cited in 3 scientific papers (total in 3 papers)

Invariant operators on a symplectic supermanifold

G. S. Shmelev


Abstract: This paper studies unary operators in tensor fields on a symplectic supermanifold that are invariant with respect to canonical changes of coordinates. The formal analogue of this problem is considered – operators in formal tensor fields. A complete classification is given for such operators in the case when the image of an operator lies in a tensor field whose fiber is the direct sum of spaces generated by the highest vector.
Figures: 5.
Bibliography: 5 titles.

Full text: PDF file (647 kB)
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English version:
Mathematics of the USSR-Sbornik, 1984, 48:2, 521–533

Bibliographic databases:

UDC: 517.43
MSC: Primary 58A05; Secondary 58A10
Received: 06.05.1982

Citation: G. S. Shmelev, “Invariant operators on a symplectic supermanifold”, Mat. Sb. (N.S.), 120(162):4 (1983), 528–539; Math. USSR-Sb., 48:2 (1984), 521–533

Citation in format AMSBIB
\Bibitem{Shm83}
\by G.~S.~Shmelev
\paper Invariant operators on a symplectic supermanifold
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 120(162)
\issue 4
\pages 528--539
\mathnet{http://mi.mathnet.ru/msb2145}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=695958}
\zmath{https://zbmath.org/?q=an:0539.58009}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 2
\pages 521--533
\crossref{https://doi.org/10.1070/SM1984v048n02ABEH002689}


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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. G. S. Shmelev, “$H(2n,m)$-invariant differential operators and irreducible $\operatorname{osp}(2,2n)$-representations”, Funct. Anal. Appl., 17:4 (1983), 323–325  mathnet  crossref  mathscinet  zmath  isi
    2. D. A. Leites, “Clifford algebras as superalgebras and quantization”, Theoret. and Math. Phys., 58:2 (1984), 150–152  mathnet  crossref  mathscinet  zmath  isi
    3. D. A. Leites, I. M. Shchepochkina, “How to Quantize the Antibracket”, Theoret. and Math. Phys., 126:3 (2001), 281–306  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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