25 citations · 57 across the 22 of their papers we have counts for
22 papers
Describing realizable Gauss diagrams using the concepts of parity or bipartate graphs
Alexei Lisitsa, Viktor Lopatkin, Alexei Vernitski
Two recent publications describe realizable Gauss diagrams using conditions stating that the number of chords in certain sets of chords is even or odd. We demonstrate that these de…
Transposed Poisson structures on Galilean and solvable Lie algebras
Ivan Kaygorodov, Viktor Lopatkin, Zerui Zhang
Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras are described. It was proven that all principal Galilean Lie algebras do not have non-trivial…
On meandric permutations
Viktor Lopatkin
We give a bijection between meanders and special sorts of Gauss diagrams which aroused from the Thurston generators of braid groups. It allows us to give an algorithm to construct…
Morse matching method for conformal cohomologies
H. Alhussein, P. Kolesnikov, V. Lopatkin
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 universal…
Garside Theory: a Composition--Diamond Lemma Point of View
Viktor Lopatkin
This paper shows how to obtain the key concepts and notations of Garside theory by using the Composition--Diamond lemma. We also show in some cases the greedy normal form is exactl…
Circle graphs (chord interlacement graphs) of Gauss diagrams: Descriptions of realizable Gauss diagrams, algorithms, enumeration
Abdullah Khan, Alexei Lisitsa, Viktor Lopatkin +1
Chord diagrams, under the name of Gauss diagrams, are used in low-dimensional topology as an important tool for studying curves or knots. Those Gauss diagrams that correspond to cu…
-derivations of Lie algebras and transposed Poisson algebras
Bruno Leonardo Macedo Ferreira, Ivan Kaygorodov, Viktor Lopatkin
A relation between -derivations of Lie algebras and transposed Poisson algebras was established. Some non-trivial transposed Poisson algebras with a certain Lie algebr…
Parafree augmented algebras and Gröbner-Shirshov bases for complete augmented algebras
Sergei O. Ivanov, Viktor Lopatkin
We develop a theory of parafree augmented algebras similar to the theory of parafree groups and explore some questions related to the Parafree Conjecture. We provide an example of…
The variety of dual mock-Lie algebras
Luisa M. Camacho, Ivan Kaygorodov, Victor Lopatkin +1
We classify all complex - and -dimensional dual mock-Lie algebras by algebraic and geometric way. Also we find all non-trivial complex -dimensional dual mock-Lie algebras.
Commutative Lie algebras and commutative cohomology in characteristic
Viktor Lopatkin, Pasha Zusmanovich
We discuss a version of the Chevalley--Eilenberg cohomology in characteristic , where the alternating cochains are replaced by symmetric ones.
Bipartite Graphs as Polynomials, and Polynomials as Bipartite Graphs (with a view towards dividing in )
Andrey Grinblat, Viktor Lopatkin
The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial , and any directed finite bipartite graph can be…
On Realizability Of Gauss Diagrams And Constructions Of Meanders
Andrey Grinblat, Viktor Lopatkin
The problem of which Gauss diagram can be realized by plane curves is an old one and has been solved in several ways. In this paper, we present a direct approach to this problem. W…
On Common Divisors of Fox Derivatives with towards to Zero Divisors of Group Rings
Viktor Lopatkin
Using Composition--Diamond Lemma we construct presentations of groups with the following property; for a fixed $1 \le i…
On Realizability of Gauss Diagrams
Andrey Grinblat, Viktor Lopatkin
The problem of which Gauss diagram can be realized by knots is an old one and has been solved in several ways. In this paper, we present a direct approach to this problem. We show…
On the homological dimensions of Leavitt path algebras with coefficients in commutative rings
V. Lopatkin, T. G. Nam
In this paper, we give sharp bounds for the homological dimensions of the Leavitt path algebra of a finite graph with coefficients in a commutative ring , as well a…
Derivations of the Leavitt path algebra W(n)
Viktor Lopatkin
The aim of this paper is to describe all inner and all outer derivations of Leavitt path algebra W(n) via explicit formulas. In fact the space of all inner and all outer derivation…
Petri Nets and its Polynomials
Andrey Grinblat, Viktor Lopatkin
For every finite Petri net, we construct a commutative polynomial in two variables and with coefficients from the semiring of natural numbers. We also present an inverse constructi…
Thurston's Operations on the Braid Groups
Viktor Lopatkin
In this paper we study Thurston's automaton on the braid groups via binary operations. These binary operations are obtained from the construction of this automaton. We study these…
Derivations of Leavitt path algebra
Viktor Lopatkin
In this paper, we describe the -module of outer derivations of the Leavitt path algebra of a row-finite graph with coefficients in an associative com…
Cohomology Rings of Plactic Monoid Algebra via Groubner-Shirshov Basis
Viktor Lopatkin
In this paper we shall calculate the cohomology ring and Hochschild's cohomology ring of plactic monoid algebra via Anick's resolution using Groubner-Shirshov basis
Homology of a Leavitt Path Algebra via Anick's Resolution
Viktor Lopatkin
The aim of this paper is to calculate the homology of a Leavitt path algebra via Anick's resolution. We show that all homology (in positive degrees) of a Leavitt path algebra is eq…
The Homology groups of right pointed sets over a partially commutative monoid
V. Lopatkin
We study the homology of pointed sets over a partially commutative monoid.