89 citations · 253 across the 20 of their papers we have counts for
20 papers
Aperiodic points for outer billiards
Anton Belyi, Alexei Kanel-Belov, Philipp Rukhovich +1
Euclidean outer billiard on a regular polygon (that is not a triangle, square or a hexagon) has aperiodic points, i.e., points where all iterates of the outer billiard map are defi…
An Indirect Method for Solving Combinatorial Problems
Margarita Shevtsova, Alexei Kanel-Belov, Mehdi Golafshan
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect m…
On finite dimensionality of homology of subalgebras of vector fields
Boris Feigin, Alexei Kanel-Belov, Anton Khoroshkin
We show that finite tensor products of modules of tensor fields are Noetherian modules over any graded Lie subalgebra of finite codimension in the Lie algebra of polynomial vector…
Representability of relatively free affine algebras over a Noetherian ring
Alexei Kanel-Belov, Louis Rowen, Uzi Vishne
Over the years questions have arisen about T-ideals of (noncommutative) polynomials. But when evaluating a noncentral polynomial in subalgebras of matrices, one often has little co…
On the Distribution function of area and perimeter for planar poisson line process
Alexei Kanel-Belov, Mehdi Golafshan, Sergey Malev +1
The challenges of examining random partitions of space are a significant class of problems in the theory of geometric transformations. Richard Miles calculated moments of areas and…
The images of multilinear and semihomogeneous polynomials on the algebra of octonions
Alexei Kanel-Belov, Sergey Malev, Coby Pines +1
The generalized L'vov-Kaplansky conjecture states that for any finite-dimensional simple algebra the image of a multilinear polynomial on is a vector space. In this paper w…
On cogrowth function of algebras and its logarithmical gap
A. J. Kanel-Belov, I. A. Melnikov, I. V. Mitrofanov
Let be an associative algebra. A finite word over alphabet is {\it-reducible} if its image in is a -linear combination of length-lexi…
Evaluations of Noncommutative Polynomials on Algebras: Methods and Problems, and the L'vov-Kaplansky Conjecture
Alexei Kanel-Belov, Sergey Malev, Louis Rowen +1
Let be a polynomial in several non-commuting variables with coefficients in a field of arbitrary characteristic. It has been conjectured that for any , for multiline…
On algorithmic unsolvability of the problem embeddability of algebraic varieties over a field of characteristic zero
A. J. Kanel-Belov, A. A. Chilikov
We show that for two afii varieties over an arbitrary field of characteristic zero, there is no general form of an algorithm for checking the presence of an embedding of one algebr…
A short proof that the free associative algebra is Hopfian
Alexei Kanel-Belov, Louis Rowen, Jie-Tai Yu
A short proof is given of the fact that various classes of algebras including the free associative algebra are Hopfian, i.e., every epimorphism is an automorphism. This further sim…
The images of Lie polynomials evaluated on matrices
Alexei Kanel-Belov, Sergey Malev, Louis Rowen
Kaplansky asked about the possible images of a polynomial in several noncommuting variables. In this paper we consider the case of a Lie polynomial. We describe all the pos…
Mathematical Competitions and Olympiads-Mathematic or Sport
Alexei Kanel-Belov
The situation surrounding the Olympiads is paradoxical. On the one hand, considerable resources are spent on the Olympiads. On the other hand, there are widespread arguments about…
Kemer's Theorem for Affine PI Algebras Over a Field of Characteristic Zero
Eli Aljadeff, Alexei Kanel-Belov, Yakov Karasik
We present a proof of Kemer's representability theorem for affine PI algebras over a field of characteristic zero.
Mathematical Student Education - "listki" or dialog?
Alexander Kovaldji, Alexei Kanel-Belov
The paper is devoted to technology of math. education in Russia in special mathematical schools ("listkovaya systema"). This system has positive sides and most classes in Russian m…
Scientific conferences of High school students: Where is myth and where is realty?
Alexei Kanel-Belov
The paper deals with popular mathematics and mathematical education of talented students. The paper is devoted to high school students mathematical conferences, problem contest for…
The Grassmann algebra in arbitrary characteristic and generalized sign
Gal Dor, Alexei Kanel-Belov, Uzi Vishne
We define a generalization of the Grassmann algebra which is well-behaved over arbitrary commutative rings , even when is not invertible. In particular, t…
The images of multilinear polynomials evaluated on matrices
Alexei Kanel-Belov, Sergey Malev, Louis Rowen
Let be a multilinear polynomial in several noncommuting variables, with coefficients in a algebraically closed field of arbitrary characteristic. In this paper we classify…
Hilbert series of PI relatively free G-graded algebras are rational functions
Eli Aljadeff, Alexei Kanel-Belov
Let G be a finite group, (g_{1},...,g_{r}) an (unordered) r-tuple of G^{(r)} and x_{i,g_i}'s variables that correspond to the g_i's, i=1,...,r. Let F<x_{1,g_1},...,x_{r,g_r}> be th…
Representability and Specht problem for G-graded algebras
Eli Aljadeff, Alexei Kanel-Belov
Let W be an associative PI algebra over a field F of characteristic zero, graded by a finite group G. Let id_{G}(W) denote the T-ideal of G-graded identities of W. We prove: 1. {[G…
Trisecant Lemma for Non Equidimensional Varieties
J. Y. Kaminski, A. Kanel-Belov, M. Teicher
The classic trisecant lemma states that if is an integral curve of $\PP^3$ then the variety of trisecants has dimension one, unless the curve is planar and has degree at least…