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## Transposed Poisson structure on Galilean and solvable Lie algebras

Journal of Geometry and Physics. 2023. No. 187. P. 1-20.

Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras are described. It is proven that all principal Galilean Lie algebras do not have non-trivial 12-derivations and as it follows they do not admit non-trivial transposed Poisson structures. Also, we proved that each complex finite-dimensional solvable Lie algebra admits a non-trivial transposed Poisson structure and a non-trivial Hom-Lie structure.

Makedonskyi I., Petravchuk A., / Cornell University. Series arXiv "math". 2013.

The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as subalgebras of this algebra. ...

Added: December 3, 2018

Bezrukavnikov R., Ivan Losev, / Cornell University. Series arXiv "math". 2017. No. 1708.01385.

Added: October 9, 2017

Feigin E., Kato S., Makedonskyi I., Journal fuer die reine und angewandte Mathematik 2020 Vol. 764 P. 181-216

We study the non-symmetric Macdonald polynomials specialized at infinity from various points of view. First, we define a family of modules of the Iwahori algebra whose characters are equal to the non-symmetric Macdonald polynomials specialized at infinity. Second, we show that these modules are isomorphic to the dual spaces of sections of certain sheaves on ...

Added: August 12, 2020

Yulia Gorginyan, Journal of Geometry and Physics 2023 Vol. 192 Article 104900

An operator I on a real Lie algebra is called a complex structure operator if and the -eigenspace is a Lie subalgebra in the complexification of . A hypercomplex structure on a Lie algebra is a triple of complex structures and K on satisfying the quaternionic relations. We call a hypercomplex nilpotent Lie algebra -solvable if there exists a sequence of -invariant subalgebrassuch that . We give examples of -solvable hypercomplex structures on a nilpotent Lie algebra and ...

Added: December 3, 2023

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

Pavutnitskiy F., Ivanov S., Zaikovskii A. et al., Journal of Algebra 2021 Vol. 586 P. 99-139

We study five different types of the homology of a Lie algebra over a commutative ring which are naturally isomorphic over fields. We show that they are not isomorphic over commutative rings, even over , and study connections between them. In particular, we show that they are naturally isomorphic in the case of a Lie ...

Added: October 7, 2021

Feigin B. L., Russian Mathematical Surveys 2017 Vol. 72 No. 4 P. 707-763

This paper discusses the main known constructions of vertex operator algebras. The starting point is the lattice algebra. Screenings distinguish subalgebras of lattice algebras. Moreover, one can construct extensions of vertex algebras. Combining these constructions gives most of the known examples. A large class of algebras with big centres is constructed. Such algebras have applications ...

Added: November 5, 2020

Cherednik I., Feigin E., Advances in Mathematics 2015 Vol. 282 P. 220-264

Given a reduced irreducible root system, the corresponding nil-DAHA is used to calculate the extremal coefficients of nonsymmetric Macdonald polynomials in the limit t→∞ and for antidominant weights, which is an important ingredient of the new theory of nonsymmetric q-Whittaker function. These coefficients are pure q-powers and their degrees are expected to coincide in the ...

Added: September 3, 2015

Ignatyev Mikhail, Petukhov A., Journal of Algebra 2021 Vol. 585 P. 501-557

Let $\mathfrak{n}$ be a locally nilpotent infinite-dimensional Lie algebra over $\mathbb{C}$. Let $\mathrm{U}(\mathfrak{n})$ and $\mathrm{S}(\mathfrak{n})$ be its respective universal enveloping algebra and symmetric algebra. Consider the Jacobson topology on the primitive spectrum of $\mathrm{U}(\mathfrak{n})$, and the Poisson topology on the primitive Poisson spectrum of $\mathrm{S}(\mathfrak{n})$.
We provide a homeomorphism between the corresponding topological spaces (at the ...

Added: October 8, 2023

Khoroshkin A., / ИТЭФ. Series "Препринты ИТЭФ". 2013.

This article contains the computation of the Lie algebra cohomology of the infinite-dimensional Lie algebra of formal vector fields with coefficients in symmetric powers of the coadjoint representation. At the same time we compute the cohomology of the Lie algebra of formal vector fields that preserve a given flag at the origin. The resulting cohomology ...

Added: September 29, 2013

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

Makedonskyi I., / Cornell University. Series arXiv "math". 2012.

We give a criterion of tameness and wildness for a finite-dimensional Lie algebra over an algebraically closed field. ...

Added: December 3, 2018

Feigin B. L., Hashizume K. undefined., Hoshino A. et al., Journal of Mathematical Physics 2009 Vol. 50 No. 9 P. 095215-1-095215-42

We introduce a unital associative algebra associated with degenerate CP1. We show that is a commutative algebra and whose Poincare' series is given by the number of partitions. Thereby, we can regard as a smooth degeneration limit of the elliptic algebra introduced by Feigin and Odesskii [Int. Math. Res. Notices 11, 531 (1997)]. Then we ...

Added: January 25, 2013

Арутюнов А. А., Kosolapov L., Finite Fields and Their Applications 2021 Vol. 76 Article 101921

In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, or G is an FC-group. In addition, we describe an algorithm to explicitly calculate all derivations of ...

Added: October 4, 2021

Васильев М., Zabrodin A., Zotov A., Nuclear Physics B - Proceedings Supplements 2020 Vol. 952 No. 114931 P. 1-20

We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians HjG with particles velocities q˙j of the classical model all ...

Added: August 20, 2020

Burman Y. M., / Cornell University. Series math "arxiv.org". 2013. No. 1309.4477.

Given a representation V of a group G, there are two natural ways of defining a representation of the group algebra k[G] in the external power V^{\wedge m}. The set L(V) of elements of k[G] for which these two ways give the same result is a Lie algebra and a representation of G. For the ...

Added: November 19, 2013

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

Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.

We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...

Added: March 9, 2014

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66

Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...

Added: August 27, 2016