• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Cohomology Rings of the Plactic Monoid via a Grobner--Shirshov basis
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
July 6, 2026
Ancient Craniiform Brachiopod: A Newly Discovered Species with a Unique Shell Shape and Lifestyle
Scientists from HSE University, MSU, and Tallinn University of Technology have studied a fossil species of ancient brachiopods that lived in a warm sea in what is now northern Estonia more than 445 million years ago. These ancient brachiopods developed a cup-shaped shell with a protective 'cap' that shielded them from overgrowth by other marine organisms. The study has been published in Palaeogeography, Palaeoclimatology, Palaeoecology.
July 2, 2026
Researchers Discover How Spelling Errors Slow Down Reading in Russian
Psycholinguists from the Centre for Language and Brain at HSE University–St Petersburg have shown that words that are frequently misspelled are processed more slowly by readers, even when presented with the correct spelling. The researchers confirmed this effect for the first time using Russian-language materials and found that response speed is most strongly linked to how confidently individuals can distinguish the correct spelling of a word from an incorrect one. The study has been published in The Mental Lexicon.
July 2, 2026
HSE Develops App for Assessing Phonological Processing in Children
Researchers at the HSE Centre for Language and Brain have developed a new digital tool for assessing children's phonological processing skills—the ZARYA (Sound Analysis of the Russian Language) test battery. It is the first standardised application in Russia designed to provide a fast and reliable assessment of children's ability to distinguish speech sounds, retain them in working memory, and perform phonemic analysis. The app runs on Android tablets and smartphones and is available for download from RuStore. Details of the test validation have been published in the Journal of Speech, Language, and Hearing Research.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Cohomology Rings of the Plactic Monoid via a Grobner--Shirshov basis

Journal of Algebra and its Applications. 2016. Vol. 15. No. 4. Article 1650082.
Lopatkin V.

In this paper, we calculate the cohomology ring and the Hochschild cohomology ring of the plactic monoid algebra via the Anick resolution using a Gröbner–Shirshov basis.

Research target: Mathematics
Language: English
DOI
Keywords: Hochschild cohomologyYoung diagramsGrobner bases
Similar publications
Proceedings of the 9th International School-Seminar on Nonlinear Analysis and Extremal Problems (NLA-2026). Irkutsk, Russia, June 22–26, 2026. Irkutsk : ISDCT SB RAS, 2026, 326 p.
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a porous layer. A porous medium is presented as an assemblage of identical spherical cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates for flow characteristics which show the specific behavior of the fluid. Our estimates are validated numerically. ...
Added: July 5, 2026
Журнал Телекоммуникации №1 за 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г. Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций. Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы. Переход к глобальному информационному ...
Added: July 4, 2026
"Труды МФТИ" Том 17, № 4 (68) (2025)
МФТИ, 2025.
абота  редакции  научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.   Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Graph Games and Logic Design
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
On Ω-stable 3-diffeomorphism with a solid or thickened surfaced basic set
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
Почти пустые симплексы и полиэдры Клейна
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2021 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Indicators of cosmonaut locomotor functions stability: A new method for ground-reaction forces analysis
Ivchenko A., Shestoperov A. I., Fomina E. V., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Платформа, управляемая событиями, для интеграции компонентов машинного зрения с операционным центром.
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Подход к оценке динамики уровня консолидированности отрасли
Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
Added: June 26, 2026
Morse matching method for conformal cohomologies
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
Anick complex, Hochschild cohomology, Hilbert and Poincare series of the Manturov (3,4)-group
Алхуссейн Х., Journal of Algebra and its Applications 2020 Vol. 20 No. 08 P. 2150134–0
Added: March 5, 2024
The Hochschild Cohomology of the Chinese Monoid Algebra
Алхуссейн Х., Algebra Colloquium 2022 Vol. 29 No. 04 P. 619–632
Added: March 5, 2024
The Anick Complex and the Hochschild Cohomology of the Manturov (2,3)-Group
Алхуссейн Х., Siberian Mathematical Journal 2020 Vol. 61 No. 1 P. 11–20
Added: March 5, 2024
On the Hochschild cohomology of universal enveloping associative conformal algebras
Алхуссейн Х., Колесников П. С., Journal of Mathematical Physics 2021 Vol. 62 No. 12 P. 0
Added: March 5, 2024
Hochschild cohomology of the Weyl conformal algebra with coefficients in finite modules
Алхуссейн Х., Колесников П. С., Journal of Mathematical Physics 2023 Vol. 64 No. 4 Article 041701
Added: March 5, 2024
Hochschild cohomology of the Weyl conformal algebra with coefficients in finite modules
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
Hochschild cohomology of Fermat type polynomials with non–abelian symmetries
Basalaev A., Ionov A., Journal of Geometry and Physics 2022 Vol. 174 Article 104450
For a polynomial f=x_1^n+…+x_N^n let Gf be the non–abelian maximal group of symmetries of f. This is a group generated by all g in GL(N,C), rescaling and permuting the variables, so that f(x)=f(g x). For any G subgroup in Gf we compute explicitly Hochschild cohomology of the category of G–equivariant matrix factorizations of f. We ...
Added: September 9, 2022
Derivations of Leavitt path algebras
Lopatkin V., Journal of Algebra 2019 Vol. 520 P. 59–89
In this paper, we describe the K-module HH1(LK(Γ)) of outer derivations of the Leavitt path algebra LK(Γ) of a row-finite graph Γ with coefficients in an associative commutative ring K with unit. We explicitly describe a set of generators of HH1(LK(Γ)) and relations among them. We also describe a Lie algebra structure of outer derivation algebra of the Toeplitz algebra. We prove that every derivation of a ...
Added: October 29, 2021
Gröbner–Shirshov Bases, Normal Forms, Combinatorial and Decision Problems in Algebra
Bokut L., Chen Y., Kalorkoti K. et al., World Scientific, 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
Grobner bases for coloured operads
Kharitonov V., Khoroshkin A., Annali di Matematica Pura ed Applicata 2022 No. 201 P. 203–241
In this work, we develop the machinery of Grobner bases for coloured operads, which allows us to establish a useful criterion of Koszulness of a coloured operad. Among the examples for which we show the existence of a quadratic Grobner basis, we consider the seminal Lie-Rinehart operad whose algebras include pairs (functions, vector fields). ...
Added: September 8, 2021
The 2-Leg Vertex in K-theoretic DT Theory
Kononov Y., Okounkov A., Osinenko A., Communications in Mathematical Physics 2021 Vol. 382 No. 3 P. 1579–1599
K-theoretic Donaldson-Thomas counts of curves in toric and many related threefolds can be computed in terms of a certain canonical 3-valent tensor, the K-theoretic equivariant vertex. In this paper we derive a formula for the vertex in the case when two out of three entries are nontrivial. We also discuss some applications of this result. ...
Added: September 8, 2021
Фридрих Энгельс
Klyukin P. N., В кн.: Новая российская энциклопедияЧ. 1: Эмаль - Япет. Т. XIX.: М.: Энциклопедия, Инфра-М, 2018. С. 21–22.
The theoretical contribution to the economics and statistics of the following prominent scientists and public figures is resurrected and described. Firstly, Marx’s associate, but largely independent figure - F. Engels, secondly, Nobel Prize winner of 1972 Kenneth J. Arrow, in ensemble with the subject article "Efficiency", thirdly, striking statistician, who concurred with E. Slutsky, - ...
Added: October 27, 2018
The Gerstenhaber–Schack complex for prestacks
Van H. D., Lowen W., Advances in Mathematics 2018 Vol. 330 P. 173–228
The aim of this work is to construct a complex which through its higher structure directly controlls deformations of general prestacks, building on the work of Gerstenhaber and Schack for presheaves of algebras. In defining a Gerstenhaber–Schack complex  for an arbitrary prestack , we have to introduce a differential with an infinite sequence of components instead of ...
Added: September 13, 2018
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit