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Standard Bases for the Universal Associative Conformal Envelopes of Kac–Moody Conformal Algebras
Algebras and Representation Theory. 2021. Vol. 25. No. 4. P. 847–867.
Колесников П. С.
Alhussein H., Kolesnikov P., Lopatkin V., Journal of Geometry and Physics 2025 Vol. 217 Article 105617
We apply discrete algebraic Morse theory to the computation of Hochschild cohomologies of associative conformal algebras. As an example, we evaluate the dimensions of the Hochschild cohomology groups with scalar coefficients of the universal associative conformal envelope U(3) of the Virasoro Lie conformal algebra relative to the associative locality bound N=3 on the generator. In contrast to the Weyl ...
Added: September 18, 2025
Алхуссейн Х., Колесников П. С., Journal of Mathematical Physics 2021 Vol. 62 No. 12 P. 0
Added: March 5, 2024
Колесников П. С., Experimental Mathematics 2022 Vol. 33 No. 1 P. 165–174
Added: March 5, 2024
Алхуссейн Х., Колесников П. С., Journal of Mathematical Physics 2023 Vol. 64 No. 4 Article 041701
Added: March 5, 2024
Алхуссейн Х., Journal of Mathematical Physics 2023 Vol. 64 No. 4 Article 041701
In this work, we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The Weyl conformal algebra is the universal associative conformal envelope of the Virasoro Lie conformal algebra relative to the locality N = 2. In order to obtain this result, we adjust the algebraic discrete Morse ...
Added: June 6, 2023
Lopatkin V., / Series arXiv "math". 2021.
This paper shows how to obtain the key concepts and notations of Garside theory by using the Composition--Diamond lemma. We also show in some cases the greedy normal form is exactly a Gröbner--Shirshov normal form and a family of a left-cancellative category is a Garside family, if and only if a suitable set of reductions ...
Added: October 29, 2021
Lopatkin V., Nam T. G., Journal of Algebra 2017 No. 481 P. 273–292
In this paper, we give sharp bounds for the homological dimensions of the Leavitt path algebra LK(E) of a finite graph E with coefficients in a commutative ring K, as well as establish a formula for calculating the homological dimensions of LK(E) when K is a commutative unital algebra over a field. ...
Added: October 29, 2021
Bokut L., Chen Y., Kalorkoti K. et al., World Scientific Publishing Co. Pte. Ltd, 2020.
The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac–Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple ...
Added: September 27, 2021
Feigin B. L., Gukov S., Journal of Mathematical Physics 2020 Vol. 61 No. 012302 P. 1–27
We take a peek at a general program that associates vertex (or chiral) algebras to smooth 4-manifolds in such a way that operations on algebras mirror gluing operations on 4-manifolds and, furthermore, equivalent constructions of 4-manifolds give rise to equivalences (dualities) of the corresponding algebras. ...
Added: May 15, 2020
Arakawa T., Kuwabara T., Fedor M., Communications in Mathematical Physics 2014 P. 1–40
We introduce the notion of an asymptotic algebra of chiral differential operators. We then construct, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone. We compute the space of global sections of this algebra, thereby proving a localization theorem for affine W-algebras ...
Added: December 10, 2014
Feigin B. L., Функциональный анализ и его приложения 2014 № 3
We study commutative vertex operator algebras. These algebras are isomorphic to certain subalgebras in Kac-Moody vertex operator algebras. We describe systems of relations and degenerations to quadratic algebras. Our approach leads to the fermionic formulas for characters. ...
Added: April 14, 2014