Yury Volkov
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View article: Degenerations of noncommutative Heisenberg algebras
Degenerations of noncommutative Heisenberg algebras Open
We give the full description of all degenerations of complex five dimensional noncommutative Heisenberg algebras. As a corollary, we have the full description of all degenerations of four dimensional anticommutative $3$-ary algebras.
View article: Graded Lie structure on cohomology of some exact monoidal categories
Graded Lie structure on cohomology of some exact monoidal categories Open
For some exact monoidal categories, we describe explicitly a connection\nbetween topological and algebraic definitions of the Lie bracket on the\nextension algebra of the unit object. The topological definition, due to\nSchwede and Hermann…
View article: On the derived category of quasi-hereditary algebras with two simple modules
On the derived category of quasi-hereditary algebras with two simple modules Open
We describe the derived Picard groups and two-term silting complexes for quasi-hereditary algebras with two simple modules. We also describe by quivers with relations all algebras derived equivalent to a quasi-hereditary algebra with two s…
View article: Graded Lie structure on cohomology of some exact monoidal categories
Graded Lie structure on cohomology of some exact monoidal categories Open
For some exact monoidal categories, we describe explicitly a connection between topological and algebraic definitions of the Lie bracket on the extension algebra of the unit object. The topological definition, due to Schwede and Hermann, i…
View article: Anticommutative Engel algebras of the first five levels
Anticommutative Engel algebras of the first five levels Open
Anticommutative Engel algebras of the first five degeneration levels are classified. All algebras appearing in this classification are nilpotent Malcev algebras.
View article: Faithful actions of braid groups by twists along ADE-configurations of\n spherical objects
Faithful actions of braid groups by twists along ADE-configurations of\n spherical objects Open
We prove that the action of a generalized braid group on an enhanced\ntriangulated categories, generated by spherical twist functors along an\nADE-configuration of $\\omega$-spherical objects, is faithful for any integer\n$\\omega \\neq 1$…
View article: Faithful actions of braid groups by twists along ADE-configurations of spherical objects
Faithful actions of braid groups by twists along ADE-configurations of spherical objects Open
We prove that the action of a generalized braid group on an enhanced triangulated categories, generated by spherical twist functors along an ADE-configuration of $ω$-spherical objects, is faithful for any integer $ω\neq 1$.
View article: Features of the natural bitumen distribution in the Kazan deposits on the territory of the Melekess depression in Tatarstan
Features of the natural bitumen distribution in the Kazan deposits on the territory of the Melekess depression in Tatarstan Open
This article presents the distribution of natural bitumen in the sediments of the Kazan tier of the middle Permian. Natural bitumens, concentrated in the Permian sediments of the Republic of Tatarstan, occur at shallow depths and are heavy…
View article: Gerstenhaber Bracket on the Hochschild Cohomology via An Arbitrary Resolution
Gerstenhaber Bracket on the Hochschild Cohomology via An Arbitrary Resolution Open
We prove formulas of different types that allow us to calculate the Gerstenhaber bracket on the Hochschild cohomology of an algebra using some arbitrary projective bimodule resolution for it. Using one of these formulas, we give a new shor…
View article: Groups generated by two twists along spherical sequences
Groups generated by two twists along spherical sequences Open
We describe all groups that can be generated by two twists along spherical sequences in an enhanced triangulated category. It will be shown that with one exception such a group is isomorphic to an abelian group generated by not more than t…
View article: Degenerations of Leibniz and Anticommutative Algebras
Degenerations of Leibniz and Anticommutative Algebras Open
We describe all degenerations of three-dimensional anticommutative algebras $\mathfrak{A}\mathfrak{c}\mathfrak{o}\mathfrak{m}_{3}$ and of three-dimensional Leibniz algebras $\mathfrak{L}\mathfrak{e}\mathfrak{i}\mathfrak{b}_{3}$ over $\math…
View article: Complete Classification of Algebras of Level Two
Complete Classification of Algebras of Level Two Open
The main result of the paper is the classification of all (nonassociative)\nalgebras of level two, i.e. such algebras that maximal chains of nontrivial\ndegenerations starting at them have length two. During this classification we\nobtain …
View article: Climate classification in the Northern Hemisphere using envelopes of temperature signals
Climate classification in the Northern Hemisphere using envelopes of temperature signals Open
Based on an analytic signal theory, the authors have developed an iterative algorithm for climate clustering using a temperature oscillation analysis. Surface temperature is selected as an integrated climate change indicator. Temperature s…
View article: How does the Sun affect the surface temperature?
How does the Sun affect the surface temperature? Open
We continue to develop a constructive idea of synchronicity as an essential factor in the solar-terrestrial relations. The results of applying this approach to a Wolf number series and a temperature series measured at 818 weather stations …
View article: Homogeneous triples for homogeneous algebras with two relations
Homogeneous triples for homogeneous algebras with two relations Open
In our preceding paper we have introduced the notion of an $s$-homogeneous triple. In this paper we use this technique to study connected $s$-homogeneous algebras with two relations. For such algebras, we describe all possible pairs $(A,M)…
View article: On the derived category of quasi-hereditary algebras with two simple\n modules
On the derived category of quasi-hereditary algebras with two simple\n modules Open
We describe the derived Picard groups and two-term silting complexes for\nquasi-hereditary algebras with two simple modules. We also describe by quivers\nwith relations all algebras derived equivalent to a quasi-hereditary algebra\nwith tw…
View article: The Variety of Two-dimensional Algebras Over an Algebraically Closed Field
The Variety of Two-dimensional Algebras Over an Algebraically Closed Field Open
The work is devoted to the variety of two-dimensional algebras over algebraically closed fields. First we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of certain algebra series in the varie…
View article: $A_{\infty}$-coderivations and the Gerstenhaber bracket on Hochschild cohomology
$A_{\infty}$-coderivations and the Gerstenhaber bracket on Hochschild cohomology Open
We show that Hochschild cohomology of an algebra over a field is a space of infinity coderivations on an arbitrary projective bimodule resolution of the algebra. The Gerstenhaber bracket is the graded commutator of infinity coderivations. …
View article: Degenerations of binary Lie and nilpotent Malcev algebras
Degenerations of binary Lie and nilpotent Malcev algebras Open
We describe degenerations of four-dimensional binary Lie algebras, and five-\nand six-dimensional nilpotent Malcev algebras over \\mathbb{C}. In particular,\nwe describe all irreducible components of these varieties.\n
View article: $s$-homogeneous algebras via $s$-homogeneous triples
$s$-homogeneous algebras via $s$-homogeneous triples Open
To study $s$-homogeneous algebras, we introduce the category of quivers with $s$-homogeneous corelations and the category of $s$-homogeneous triples. We show that both of these categories are equivalent to the category of $s$-homogeneous a…
View article: Sun’s effect on the surface temperature in the Northern Hemisphere
Sun’s effect on the surface temperature in the Northern Hemisphere Open
Series of temperatures measured at 818 weather stations in the Northern Hemisphere and one series of Wolf numbers for the period from 1955 to 2010 are considered. The sun's effect on the surface temperature is estimated by the cosine of th…
View article: The degeneration level classification of algebras
The degeneration level classification of algebras Open
The aim of the paper is to develop methods that will allow to classify algebras of small levels, i.e. such algebras that all chains of nontrivial degenerations starting at them have relatively small lengths. Accordingly, the algebra under …
View article: Generating degrees for graded projective resolutions
Generating degrees for graded projective resolutions Open
We provide a framework connecting several well-known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras…
View article: Degenerations of Zinbiel and nilpotent Leibniz algebras
Degenerations of Zinbiel and nilpotent Leibniz algebras Open
We describe degenerations of four-dimensional Zinbiel and four-dimensional\nnilpotent Leibniz algebras over C. In particular, we describe all irreducible\ncomponents in the corresponding varieties.\n
View article: On variants of linearity of graded modules
On variants of linearity of graded modules Open
We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras…
View article: Generating degrees for graded projective resolutions
Generating degrees for graded projective resolutions Open
We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras…