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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2026. Vol 56

Hochschild Cohomology of the Algebra of Conformal Endomorphisms

Author(s)

Pavel S. Kolesnikov 1, Hassan Alhussein 2,3,4

1 Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation

2 Siberian State University of Telecommunication and Informatics, Novosibirsk, Russian Federation

3 Novosibirsk State University of Economics and Management, Novosibirsk, Russian Federation

4 Novosibirsk State University, Novosibirsk, Russian Federation

Abstract
It was proved by I. Dolguntseva (St. Peterburg Math. J., 2010) that second Hochschild cohomology groups for the associative conformal algebra 𝐶𝑒𝑛𝑑𝑘 with coefficients in an arbitrary conformal bimodule are trivial. In this work, we prove the same for all higher Hochschild cohomologies of 𝐶𝑒𝑛𝑑𝑘 by means of algebraic discrete Morse theory applied to the bar complex of the 1st Weyl algebra.
About the Authors

Pavel S. Kolesnikov, Dr. Sci. (Phys.-Math.), Prof., Sobolev Institute of Mathematics SB RAS, Novosibirsk, 630090, Russian Federation, Pavel77@gmail.com

Hassan Alhussein, Cand. Sci. (Phys.Math.), Assoc. Prof., Siberian State University of Telecommunication and Informatics, Novosibirsk, 630102, Russian Federation, k.alhussein@g.nsu.ru

For citation
Kolesnikov P. S., Alhussein H. Hochschild Cohomology of the Algebra of Conformal Endomorphisms. The Bulletin of Irkutsk State University. Series Mathematics, 2026, vol. 56, pp. 129–144. https://doi.org/10.26516/1997-7670.2026.56.129
Keywords
conformal algebra, Hochschild cohomology, Groebner–Shirshov basis, Morse matching
UDC
512.552:517.54
MSC
16E40, 17B68, 17B69, 16W25
DOI
https://doi.org/10.26516/1997-7670.2026.56.129
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