25 citations · 57 across the 22 of their papers we have counts for
9 papers · 1 filter
Hochschild cohomology of Temperley--Lieb algebras: a Kauffman diagram perspective
Viktor Lopatkin
We describe Hochschild cohomology of Temperley--Lieb algebras by explicit minimal-resolution coordinates and multilinear operations on Kauffman diagrams. For each doubled-line basi…
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…
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…
-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.
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 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…