Triviality of the second cohomology group of the conformal algebras 𝐶𝑒𝑛𝑑_{𝑛} and 𝐶𝑢𝑟_{𝑛}

Dolguntseva, I.

doi:10.1090/S1061-0022-09-01085-1

Triviality of the second cohomology group of the conformal algebras $\mathrm {Cend}_n$ and $\mathrm {Cur}_n$
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by I. A. Dolguntseva
Translated by: the author

St. Petersburg Math. J. 21 (2010), 53-63

DOI: https://doi.org/10.1090/S1061-0022-09-01085-1

Published electronically: November 4, 2009

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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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