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Uspekhi Mat. Nauk, 1969, Volume 24, Issue 4(148), Pages 3–64 (Mi umn5520)  

This article is cited in 9 scientific papers (total in 9 papers)

Classification of representanions of the anticommutation relations

V. Ya. Golodets


Abstract: The paper deals with the classification of representations of the anticommutation relations in the “space of occupation numbers”. The problem reduces to the determination of all the realizations of a certain denumerable discrete commutative group as a group of automorphisms of a measure space leaving the measure quasiinvariant, and also to the construction of such measures.

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English version:
Russian Mathematical Surveys, 1969, 24:4, 1–63

Bibliographic databases:

UDC: 519.4+519.9
MSC: 81S05, 20F12, 15A27
Received: 17.02.1969

Citation: V. Ya. Golodets, “Classification of representanions of the anticommutation relations”, Uspekhi Mat. Nauk, 24:4(148) (1969), 3–64; Russian Math. Surveys, 24:4 (1969), 1–63

Citation in format AMSBIB
\Bibitem{Gol69}
\by V.~Ya.~Golodets
\paper Classification of representanions of the anticommutation relations
\jour Uspekhi Mat. Nauk
\yr 1969
\vol 24
\issue 4(148)
\pages 3--64
\mathnet{http://mi.mathnet.ru/umn5520}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=264409}
\zmath{https://zbmath.org/?q=an:0186.46305|0202.13301}
\transl
\jour Russian Math. Surveys
\yr 1969
\vol 24
\issue 4
\pages 1--63
\crossref{https://doi.org/10.1070/RM1969v024n04ABEH001351}


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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. F. A. Berezin, “Some notes on representations of the commutation relations”, Russian Math. Surveys, 24:4 (1969), 65–88  mathnet  crossref  mathscinet  zmath
    2. O. I. Zavialov, V. N. Sushko, “Canonical variables in the physics of in finite systems”, Theoret. and Math. Phys., 1:2 (1969), 119–138  mathnet  crossref  mathscinet
    3. V. Ya. Golodets, “Classes of approximately finite factors”, Funct. Anal. Appl., 4:4 (1970), 276–281  mathnet  crossref  mathscinet  zmath
    4. A. M. Stepin, “Cohomologies of automorphism groups of a Lebesgue space”, Funct. Anal. Appl., 5:2 (1971), 167–168  mathnet  crossref  mathscinet  zmath
    5. V. Ya. Golodets, “Modular operators and asymptotic commutativity in von Neumann algebras”, Russian Math. Surveys, 33:1 (1978), 47–106  mathnet  crossref  mathscinet  zmath
    6. S. A. Kruglyak, Yu. S. Samoilenko, “Unitary equivalence of sets of self-adjoint operators”, Funct. Anal. Appl., 14:1 (1980), 48–50  mathnet  crossref  mathscinet  zmath
    7. R. S. Ismagilov, “Riesz products and spectrum of Mackey actions”, Funct. Anal. Appl., 20:3 (1986), 242–244  mathnet  crossref  mathscinet  zmath  isi
    8. R. S. Ismagilov, “Application of the group algebra of the problem of the tail $\sigma$-algebra of a random walk on a group and the problem of ergodicity of a skew-product action”, Math. USSR-Izv., 31:1 (1988), 209–222  mathnet  crossref  mathscinet  zmath
    9. E. Galina, A. Kaplan, L. Saal, “Charged Representations of the Infinite Fermi and Clifford Algebras”, Lett Math Phys, 72:1 (2005), 65  crossref  mathscinet  zmath  adsnasa  isi
  • Успехи математических наук Russian Mathematical Surveys
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