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Rings of Fractions of Reduction Algebras
Algebras and Representation Theory. 2013. P. 1–10.
Khoroshkin S. M., Ogievetsky O.
In press
We establish the absence of zero divisors in the reduction algebra of a Lie algebra {Mathematical expression} with respect to its reductive Lie subalgebra {Mathematical expression}. We identify the field of fractions of the diagonal reduction algebra of {Mathematical expression} with the standard skew field; as a by-product we obtain a two-parametric family of realizations of this diagonal reduction algebra by differential operators. We also present a new proof of the Poincaré-Birkhoff-Witt theorem for reduction algebras.
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Merkulov S., Journal of Pure and Applied Algebra 2023 Vol. 227 No. 10 P. 1–47
Added: December 19, 2025
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
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
Lopatkin V., Kaygorodov I., Zhang Z., 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. ...
Added: May 5, 2023
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
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
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
Feigin E., Journal of Lie Theory 2019 Vol. 29 No. 4 P. 927–940
The Littlewood-Richardson coefficients describe the decomposition of tensor products of irreducible representations
of a simple Lie algebra into irreducibles. Assuming the number of factors is large, one gets a measure on the space of weights. This limiting measure was extensively studied by many authors. In particular, Kerov computed the corresponding density in a special case in ...
Added: December 9, 2019
Makedonskyi I., / 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
Makedonskyi I., Petravchuk A., / 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
Khoroshkin S. M., Огиевецкий О. В., Journal of Geometry and Physics 2018 Vol. 129 P. 99–116
We define contravariant forms on diagonal reduction algebras, algebras of h-deformed differential operators and on standard modules over these algebras. We study properties of these forms and their specializations. We show that the specializations of the forms on the spaces of h-commuting variables present zero singular vectors iff they are in the kernel of the ...
Added: August 1, 2018
Shirokov D., , in: Proceedings of the Nineteenth International Conference on Geometry, Integrability and QuantizationVol. 19.: Sofia: Avangard Prima, 2018. Ch. 1 P. 11–53.
We discuss some well-known facts about Clifford algebras: matrix representations, Cartan’s periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in <span data-mathml="nn dimensions, etc. We also present our point of view on some problems. Namely, we discuss the generalization of the Pauli theorem, the basic ideas of the ...
Added: January 31, 2018