Abstract:
It is proved that the second cohomology group of the conformal algebras Cendn and Curn with coefficients in any bimodule is trivial. As a result, these algebras are segregated in any extension with a nilpotent kernel.
Keywords:
associative conformal algebra, algebra of conformal endomorphisms, Hochschild cohomology.
Citation:
I. A. Dolguntseva, “Triviality of the second cohomology group of the conformal algebras Cendn and Curn”, Algebra i Analiz, 21:1 (2009), 74–89; St. Petersburg Math. J., 21:1 (2010), 53–63
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\by I.~A.~Dolguntseva
\paper Triviality of the second cohomology group of the conformal algebras $\mathrm{Cend}_n$ and $\mathrm{Cur}_n$
\jour Algebra i Analiz
\yr 2009
\vol 21
\issue 1
\pages 74--89
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\jour St. Petersburg Math. J.
\yr 2010
\vol 21
\issue 1
\pages 53--63
\crossref{https://doi.org/10.1090/S1061-0022-09-01085-1}
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Linking options:
https://www.mathnet.ru/eng/aa862
https://www.mathnet.ru/eng/aa/v21/i1/p74
This publication is cited in the following 8 articles:
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Bo Hou, Zhongxi Shen, Jun Zhao, “Gerstenhaber algebra of the Hochschild cohomology of an associative conformal algebra”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 117:2 (2023)
R. A. Kozlov, “Tochnye predstavleniya konechnogo tipa konformnykh algebr Li”, Algebra i logika, 62:3 (2023), 408–414
Lamei Yuan, “O-operators and Nijenhuis operators of associative conformal algebras”, Journal of Algebra, 609 (2022), 245
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
R. A. Kozlov, “Hochschild cohomologies of the associative conformal algebra Cend1,x”, Algebra and Logic, 58:1 (2019), 36–47
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
Zhang J., “on the Cohomology of Leibniz Conformal Algebras”, J. Math. Phys., 56:4 (2015), 041703
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