Hassan Alhussein ; Pavel Kolesnikov ; Viktor Lopatkin
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Hochschild cohomology of the universal associative conformal envelope of
the Virasoro Lie conformal algebra with coefficients in all finite modules
cm:14674 -
Communications in Mathematics,
January 9, 2025,
Volume 33 (2025), Issue 3 (Special issue: European Non-Associative Algebra Seminar)
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https://doi.org/10.46298/cm.14674
Hochschild cohomology of the universal associative conformal envelope of
the Virasoro Lie conformal algebra with coefficients in all finite modulesArticle
Authors: Hassan Alhussein ; Pavel Kolesnikov ; Viktor Lopatkin
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Hassan Alhussein;Pavel Kolesnikov;Viktor Lopatkin
In this paper, we find the Hochschild cohomology groups of the universal
associative conformal envelope $U(3)$ of the Virasoro Lie conformal algebra
with respect to associative locality $N=3$ on the generator with coefficients
in all finite modules. In order to obtain this result, we construct the Anick
resolution via the algebraic discrete Morse theory and Gröbner--Shirshov
basis.