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Algebra Logika, 2007, Volume 46, Number 6, Pages 688–706 (Mi al321)  

This article is cited in 5 scientific papers (total in 5 papers)

Hochschild cohomologies for associative conformal algebras

I. A. Dolguntseva

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We introduce the concept of Hochschild cohomologies for associative conformal algebras. It is shown that the second cohomology group of a conformal Weyl algebra with values in any bimodule is trivial. As a consequence, we derive that the conformal Weyl algebra is segregated in any extension with nilpotent kernel.

Keywords: conformal algebra, cohomology group, Weyl algebra.

Full text: PDF file (201 kB)
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English version:
Algebra and Logic, 2007, 46:6, 373–384

Bibliographic databases:

UDC: 512.664.2
Received: 22.01.2007

Citation: I. A. Dolguntseva, “Hochschild cohomologies for associative conformal algebras”, Algebra Logika, 46:6 (2007), 688–706; Algebra and Logic, 46:6 (2007), 373–384

Citation in format AMSBIB
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\by I.~A.~Dolguntseva
\paper Hochschild cohomologies for associative conformal algebras
\jour Algebra Logika
\yr 2007
\vol 46
\issue 6
\pages 688--706
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2389419}
\zmath{https://zbmath.org/?q=an:1155.16300}
\transl
\jour Algebra and Logic
\yr 2007
\vol 46
\issue 6
\pages 373--384
\crossref{https://doi.org/10.1007/s10469-007-0037-8}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. A. Dolguntseva, “Triviality of the second cohomology group of the conformal algebras $\mathrm{Cend}_n$ and $\mathrm{Cur}_n$”, St. Petersburg Math. J., 21:1 (2010), 53–63  mathnet  crossref  mathscinet  zmath  isi
    2. Zhang J., “on the Cohomology of Leibniz Conformal Algebras”, J. Math. Phys., 56:4 (2015), 041703  crossref  mathscinet  zmath  isi  elib  scopus
    3. P. S. Kolesnikov, R. A. Kozlov, “Molien–Wedderburn theorem for associative conformal algebras with finite faithful representation”, Algebra and Logic, 56:5 (2017), 427–428  mathnet  crossref  crossref  isi
    4. R. A. Kozlov, “Hochschild cohomologies of the associative conformal algebra $\mathrm{Cend}_{1,x}$”, Algebra and Logic, 58:1 (2019), 36–47  mathnet  crossref  crossref  isi
    5. Kolesnikov P.S., Kozlov R.A., “on the Hochschild Cohomologies of Associative Conformal Algebras With a Finite Faithful Representation”, Commun. Math. Phys., 369:1 (2019), 351–370  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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