?
Весовые системы и инварианты графов и вложенных графов
Успехи математических наук. 2022. Т. 77. № 5(467). С. 131-184.
Keywords: алгебра Хопфавесовая системаалгебра Лиинвариант графовинвариант узлов и зацепленийвложенный графдельта-матроид
Publication based on the results of:
Zinova P., Функциональный анализ и его приложения 2020 Т. 54 № 3 С. 73-93
A weight system is a function on chord diagrams that satisfies the so-called four-term
relations. Vassiliev’s theory of finite-order knot invariants describes these invariants in terms of
weight systems. In particular, there is a weight system corresponding to the colored Jones polynomial.
This weight system can be easily defined in terms of the Lie algebra sl2, but this ...
Added: December 10, 2020
N.G. Chebochko, Russian Mathematics 2021 Vol. 65 No. 8 P. 75-78
The study of deformations of Lie algebras is related to the problem of classification
of simple Lie algebras over fields of small characteristics. The classification of finite-dimensional
simple Lie algebras over algebraically closed fields of characteristic p > 3 is completed. Over
fields of characteristic 2, a large number of examples of Lie algebras are constructed that do
not ...
Added: September 27, 2021
Arzhantsev I., Успехи математических наук 2001 Т. 56 № 3 С. 155-156
Added: July 9, 2014
Glutsyuk A., Israel Journal of Mathematics 2023 Vol. 258 No. 1 P. 137-184
Reflections from hypersurfaces act by symplectomorphisms on the space of oriented lines with respect to the canonical symplectic form. We consider an arbitrary infinitely-smooth hypersurface in Euclidean space that is either a global strictly convex closed hypersurface, or a germ of hypersurface. We deal with the pseudogroup generated by compositional ratios of reflections from it ...
Added: November 4, 2021
Akbarov S. S., De Gruyter, 2022
The term "stereotype space" was introduced in 1995 and is used for a category of locally convex spaces with surprisingly elegant properties. Its study gives an unexpected point of view on functional analysis that brings this field closer to other main branches of mathematics, namely, to algebra and geometry.
This volume contains:
the foundations of the theory ...
Added: June 1, 2022
Zinova P., Математический сборник 2022 Т. 213 № 2 С. 115-148
Теорема Чмутова--Ландо утверждает, что значение весовой системы (функции на хордовых диаграммах, удовлетворяющей 4-членным соотношениям Васильева), отвечающей алгебре Ли $\mathfrak{sl}_2$, зависит лишь от графа пересечений хордовой диаграммы.
В настоящей статье мы вычисляем значения $\mathfrak{sl}_2$-весовой системы на графах нескольких бесконечных серий, представляющих собой соединение графа с малым числом вершин с дискретным. В частности, мы вычисляем эти значения для ...
Added: October 11, 2021
Shirokov D., Advances in Applied Clifford Algebras 2012 Vol. 22 No. 1 P. 243-256
We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing commutators and anticommutators of Clifford algebra elements. This method allows us to find out and prove a number of new properties of Clifford algebra elements. ...
Added: June 16, 2015
Arzhantsev I., Liendo A., Stasyuk T., Journal of Pure and Applied Algebra 2021 Vol. 225 No. 2 P. 106499
Let X be a normal variety endowed with an algebraic torus action. An additive group action alpha on X is called vertical if a general orbit of alpha is contained in the closure of an orbit of the torus action and the image of the torus normalizes the image of alpha in Aut(X). Our first result in this paper ...
Added: July 29, 2020
МЦНМО, 2017
Шестая школа-конференция «Алгебры Ли, алгебраические группы и тео- рия инвариантов» проходила в Москве с 30 января по 4 февраля 2017 года. Её организаторами были Московский государственный университет имени М.В. Ломоносова, Самарский национальный исследовательский университет имени академика С.П. Королёва, Совместная Русско-Французская лаборато- рия им. Ж.-В. Понселе и Международная лаборатория зеркальной симмет- рии и автоморфных форм Высшей ...
Added: September 11, 2017
Shabalin T., Сибирский математический журнал 2013 Т. 54 № 4 С. 947-958
Under study are the centralizers of 3-dimensional simple Lie subalgebras in the universal enveloping algebra of a 7-dimensional simple Malcev algebra. We find some sets of generators for these centralizers in characteristic not 2 nor 3 and for the subalgebra generated by the centralizer in the central closure of the universal enveloping algebra in characteristic ...
Added: September 16, 2014
Nadezhda Kodaneva, / Cornell University. Series math "arxiv.org". 2019. No. arXiv:2002.12440.
In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and determines thus a finite type invariant of links in the 3-sphere. ...
Added: December 14, 2020
Kodaneva N., Moscow Mathematical Journal 2020
In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and determines thus a finite type invariant of links in the 3-sphere. ...
Added: November 20, 2020
Zhukov V., Функциональный анализ и его приложения 2018 Т. 52 № 2 С. 15-24
Инварианты конечного порядка (инварианты Васильева) узлов выражаются в терминах весовых систем — функций на хордовых диаграммах (вложенных графах с одной вершиной), удовлетворяющих четырехчленным соотношениям. У весовых систем имеется графовый аналог — -инварианты графов, т.е. функции на графах, удовлетворяющие четырехчленному соотношению для графов. Каждый -инвариант определяет весовую систему.
Понятие весовой системы естественно обобщается на случай вложенных графов с произвольным ...
Added: December 15, 2017
Shirokov D., Journal of Geometry and Symmetry in Physics 2016 Vol. 42 P. 73-94
In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove isomorphisms between these groups and classical matrix groups (symplectic, orthogonal, linear, unitary) in the cases of arbitrary dimension and arbitrary signature. Also we obtain isomorphisms of corresponding Lie algebras ...
Added: December 14, 2016
Switzerland : Birkhauser/Springer, 2019
Lie theory, inaugurated through the fundamental work of Sophus Lie during the late
nineteenth century, has proved central in many areas of mathematics and theoretical
physics. Sophus Lie’s formulation was originally in the language of analysis and
geometry; however, by now, a vast algebraic counterpart of the theory has been
developed. As in algebraic geometry, the deepest and most ...
Added: October 26, 2019
Chmutov S., Kazaryan M., Lando S., Selecta Mathematica, New Series 2020 Vol. 26 No. 3 P. 1-22
We prove that the generating function for the symmetric chromatic polynomial of all simple graphs is (after an appropriate scaling change of variables) a linear combination of one-part Schur polynomials. This statement immediately implies that it is also a tau-function of the Kadomtsev–Petviashvili integrable hierarchy of mathematical physics. Moreover, we describe a large family of ...
Added: June 9, 2020
Shirokov D., Advances in Applied Clifford Algebras 2010 Vol. 20 No. 2 P. 411-425
In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we consider subalgebras of Lie algebras of pseudo-unitary groups. Our main techniques are Clifford algebras. We have found 12 types of subalgebras of Lie algebras of pseudo-unitary groups. ...
Added: June 16, 2015
Pirkovskii A. Y., / Cornell University. Series math "arxiv.org". 2011. No. 1101.0166.
Given a Hopf algebra H and an H-module algebra A, we explicitly describe the Arens-Michael envelope of the smash product A#H in terms of the Arens-Michael envelope of H and a certain completion of A. We also give an example (Manin's quantum plane) showing that the result fails for non-Hopf bialgebras. ...
Added: March 12, 2013
Р.С. Авдеев, Труды Московского математического общества 2010 Т. 71 С. 235-269
A spherical homogeneous space G/H of a connected semisimple algebraic group G is called excellent if it is quasi-affine and its weight semigroup is generated by disjoint linear combinations of the fundamental weights of the group G. All the excellent affine spherical homogeneous spaces are classified up to isomorphism. ...
Added: February 25, 2014
Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016
The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...
Added: November 2, 2016
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253
Added: December 22, 2016
Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.
We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...
Added: September 29, 2019
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020