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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

Triviality of the second cohomology group of the conformal algebras $ \mathrm{Cend}_n$ and $ \mathrm{Cur}_n$


Author: I. A. Dolguntseva
Translated by: the author
Original publication: Algebra i Analiz, tom 21 (2009), nomer 1.
Journal: St. Petersburg Math. J. 21 (2010), 53-63
MSC (2000): Primary 13D03
Published electronically: November 4, 2009
MathSciNet review: 2553052
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Abstract: It is proved that the second cohomology group of the conformal algebras $ \operatorname{Cend}_n$ and $ \operatorname{Cur}_n$ with coefficients in any bimodule is trivial. As a result, these algebras are segregated in any extension with a nilpotent kernel.


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Additional Information

I. A. Dolguntseva
Affiliation: Sobolev Institute of Mathematics, Akademician Koptyug Prospekt 4, 630090 Novosibirsk, Russia
Email: irina.dolgunceva@gmail.com

DOI: http://dx.doi.org/10.1090/S1061-0022-09-01085-1
PII: S 1061-0022(09)01085-1
Keywords: Associative conformal algebra, algebra of conformal endomorphisms, Hochschild cohomology.
Received by editor(s): February 5, 2008
Published electronically: November 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society