Длина групповой алгебры прямого произведения циклической группы и циклической p-группы в модулярном случае

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Длина групповой алгебры прямого произведения циклической группы и циклической p-группы в модулярном случае

Записки научных семинаров ПОМИ РАН. 2023. Т. 524. С. 166–176.

Хрыстик М. А.

конечномерные алгебры, длина алгебры, групповые алгебры, абелевы группы, $p$-группы [finite-dimensional algebras, length of an algebra, group algebras, abelian groups, $p$-groups]

Research target: Mathematics

Language: Russian

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Mathematical methods inthe studies of definitional complexity, computational complexity and formal language (2023)

Моделирование полностью роботизированного склада со стеллажами глубокого хранения

Gadzhimirzaev S., Хельвас А. В., Computer Research and Modeling 2026 Vol. 18 No. 2 P. 423–438

This article presents a model of a fully automated warehouse with deep storage racks designed for boxed goods storage. The study focuses on optimizing warehouse operations through discrete multiagent simulation of shuttle movements for pallet loading and unloading tasks. The authors investigate various product placement strategies, including the Nearest Channel Positioning Algorithm (NCPA), Most Empty ChannelGroup Placement (MECGP), and ...

Added: June 24, 2026

Нахождение формальных степенно–логарифмических разложений решений 𝑞–разностных уравнений

Gaianov N., Parusnikova A., Уфимский математический журнал 2026 Т. 18 № 2 С. 14–22

We consider an algebraic 𝑞–difference equation. We propose a sufficient condition for the existence of a formal power–logarithmic expansion in the vicinity of zero of the solution to such an equation. We apply this sufficient condition to construct the formal expansion of a solution to a certain 𝑞–difference analogue of the fifth Painlevé equation for particular ...

Added: June 24, 2026

Open r-spin theory II: The analogue of Witten's conjecture for r-spin disks

Buryak A., Clader E., Tessler R., Journal of Differential Geometry 2024 Vol. 128 No. 1 P. 1–75

We conclude the construction of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open $r$-spin intersection numbers, and we prove that their generating function is closely related to the wave function of the $r$th Gelfand--Dickey integrable hierarchy. This provides an analogue of Witten's $r$-spin conjecture in the open setting ...

Added: June 23, 2026

Tautological relations and integrable systems

Buryak A., Shadrin S., Epijournal de Geometrie Algebrique 2024 Vol. 8

We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus g with n marked points. A large part of these relations has a surprisingly simple form: the tautological classes involved in the relations are given by stable graphs that are trees and that are decorated only by powers ...

Added: June 23, 2026

Counting meromorphic differentials on $CP^1$

Buryak A., Rossi P., Letters in Mathematical Physics 2024 Vol. 114 Article 97

We give explicit formulas for the number of meromorphic differentials on $CP^1$ with two zeros and any number of residueless poles and for the number of meromorphic differentials on $CP^1$ with one zero, two poles with unconstrained residue and any number of residueless poles, in terms of the orders of their zeros and poles. These ...

Added: June 23, 2026

Moduli spaces of residueless meromorphic differentials and the KP hierarchy

Buryak A., Rossi P., Zvonkine D., Geometry and Topology 2024 Vol. 28 P. 2793–2824

We prove that the cohomology classes of the moduli spaces of residueless meromorphic differentials, ie the closures, in the moduli space of stable curves, of the loci of smooth curves whose marked points are the zeros and poles of prescribed orders of a meromorphic differential with vanishing residues, form a partial cohomological field theory (CohFT) of ...

Added: June 23, 2026

DR-иерархии: от пространств модулей кривых к интегрируемым системам

Buryak A., Труды Математического института им. В.А. Стеклова РАН 2024 Т. 325 С. 26–66

The main goal of the paper is to show that the DR hierarchies, introduced by the author in an earlier paper, allow one to establish, in the most clear way, a relation between the topology of the Deligne–Mumford compactification of the moduli space of smooth algebraic curves of genus g with n marked points and integrable systems ...

Added: June 23, 2026

Growth in noncommutative algebras and entropy in derived categories

Piontkovski D., / Series arXiv "math". 2026.

A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...

Added: June 23, 2026

Multilinear nilalgebras and the Jacobian theorem

Piontkovski D., / Series arXiv "math". 2025.

If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...

Added: June 23, 2026

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Калужский печатный двор, 2026.

Conference Proceedings INTERNATIONAL CONFERENCE “Mathematical Ideas of Academician P.L. Chebyshev, Their Applications in Natural Sciences and Artificial Intelligence Technologies” dedicated to the 205th anniversary of his birth ...

Added: June 20, 2026

Численное решение уравнений Блэка–Шоулза и конвекции-диффузии с определением положения свободной границы

Джанбекова А. Р., Shvedov A. S., Математическое моделирование 2026 Т. 38 № 3 С. 159–176

Boundary value problems for the Black–Scholes partial differential equation, which describes the value of a financial instrument, may contain a free boundary condition if the financial instrument allows for early exercise. This article considers free boundary value problems for the Black–Scholes equation and the convection diffusion equation. For the convection diffusion equation, a finite difference ...

Added: June 20, 2026

Open Hurwitz numbers and the mKP hierarchy

Buryak A., Tessler R., Troshkin M., Journal of Geometry and Physics 2026 Vol. 223 Article 105783

We give a natural definition of open Hurwitz numbers, where the weight of each ramified covering includes an integer parameter N taken to the power that is equal to the number of boundary components of a Riemann surface with boundary mapping to . We prove that the resulting sequence of partition functions, depending on , is a tau-sequence of ...

Added: June 19, 2026

Bihamiltonian structure of the DR hierarchy in the semisimple case

Buryak A., Rossi P., Communications in Mathematical Physics 2025 Vol. 406 Article 205

Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the second has the advantage of being very explicit. The Poisson operator of the DR hierarchy is , where is the metric ...

Added: June 19, 2026

Advances in Information Retrieval: 48th European Conference on Information Retrieval, ECIR 2026, Delft, The Netherlands, March 29 – April 2, 2026, Proceedings, Part II. (LNCS, volume 16484)

Cham: Springer Publishing Company, 2026.

The four-volume set LNCS 16483-16486 constitutes the refereed conference proceedings of the 48th European Conference on Information Retrieval, ECIR 2026, held in Delft, The Netherlands, during March 29–April 2, 2026. The 46 full papers and 37 short papers presented together with 10 findings papers, 9 reproducibility papers, 17 resource papers, 11 workshop papers, 7 tutorial papers, ...

Added: June 18, 2026

Искусственный интеллект как роза научной деятельности: исследование Тимоти Гауэрса

Poddiakov A., Троицкий вариант. Наука 2026 № 12 С. 24–25

В научно-популярной заметке представлен обзор содержания поста филдсовского медалиста Тимоти Гауэрса о возможностях ИИ в математике и содержания комментариев под постом. Обзор сделан в основном чат-ботом DeepSeek. В заключение обсуждается возможность не только решения задач искусственным интеллектом, но и их постановки. ...

Added: June 18, 2026

Optimal Extraction with an Impact on Diffusion-Jump Pricing

Garzón J., Mora Rodríguez J., Moreno-Franco H. A., Applied Mathematics and Optimization 2026 Vol. 94 No. 10 P. 1–43

We study an optimal extraction problem where the agent’s actions in the spot market exert an additive proportional negative impact on the commodity price. The commodity price dynamics, prior to any activity by the agent, evolve according to a drifted Brownian motion with jumps. The agent’s primary aim is to identify an optimal extraction strategy ...

Added: June 17, 2026

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Nesterov A. S., Журнал Новой экономической ассоциации 2026

В этой статье рассматривается целевой приём в вузы в России с точки зрения науки об устройстве рынков сочетания и экономических механизмов (matching market and mechanism design), ключевого направления современной теории игр. Мы изучаем механизм целевого приёма -- набор правил, по которым устраивается трёхстороннее сочетание между абитуриентом, заказчиком и образовательной программой. Используемый в России механизм имеет ...

Added: June 16, 2026

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Благовещенская Е. А., Павлова Н. Г., Гарбарук В. В. et al., Международная конференция по мягким вычислениям и измерениям 2018 Т. 1 С. 684–686

Abelian torsion-free groups, being one of the primary algebraic structures, admit an algorithmic approach to the study of their various direct decompositions. The graphs used are of the line-parallel form and they are applicable to parallelization problems. ...

Added: January 13, 2026

COMMON FEATURES OF ALGORITHMIC APPROACHES TO SUB-WORD PARALLELISM AND TORSION-FREE ABELIAN GROUP DECOMPOSITIONS

Благовещенская Е. А., Гарбарук В. В., Кузнецова И. В. et al., , in: IEEE International Conference on Electrical Engineering and Photonics (EExPolytech).: St. Petersburg: IEEE, 2021. P. 128–131.

Added: January 13, 2026

NEAR ISOMORPHISM FOR COUNTABLE-RANK TORSION-FREE ABELIAN GROUPS

Благовещенская Е. А., Филимонов А. В., Трифонов А. Е., Journal of Mathematical Sciences 2021 Vol. 259 No. 4 P. 394–402

Added: January 13, 2026

Завершение классификации инволютивных двузначных групп

Гугнин Д. В., Алгебра и анализ 2025 Т. 37 № 6 С. 90–99

В работе В. М. Бухштабера, А. П. Веселова и А. А. Гайфуллина 2022 года была получена практически полная классификация инволютивных коммутативных двузначных групп. В работе А. А. Гайфуллина 2024 года была доказана автоматическая коммутативность произвольной инволютивной двузначной группы. Единственный вопрос о классификации инволютивных двузначных групп, который оставался открытым после этих публикаций, заключается в следующем: Верно ли, что если две ...

Added: November 13, 2025

Finite abelian groups acting on rationally connected threefolds II: groups of K3 type

Loginov K., Zhang Z., Pinardin A., / Series arXiv "math". 2025.

We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular, if a finite abelian group faithfully acts on a threefold preserving a K3 surface (with at worst ...

Added: September 27, 2025

Длина групповой алгебры прямого произведения циклической группы и элементарной абелевой p-группы в модулярном случае

Хрыстик М. А., Сибирские электронные математические известия 2024 Т. 21 № 2 С. 1132–1144

In this paper, the length of the group algebra of the direct product of a cyclic group and an elementary abelian p-group over a eld of characteristic p is calculated. ...

Added: December 11, 2024

A proof of the Paz conjecture for 6 × 6 matrices

M.A. Khrystik, A.M. Maksaev, Linear Algebra and its Applications 2025 Vol. 704 P. 249–269

Let Mn(F) be the algebra of n×n matrices over a field F and let S be its generating set (as an F-algebra). The length of S is the smallest number k such that Mn(F) equals the F-linear span of all products of the length at most k of matrices from S. The length of Mn(F), denoted by l(Mn(F)), is defined to be the maximal length of any of its generating sets. In 1984, Paz conjectured that l(Mn(F))=2n−2, ...

Added: November 22, 2024