A5042138891- Algebraic structures and combinatorial models
- Advanced Topics in Algebra
- Homotopy and Cohomology in Algebraic Topology
- Advanced Operator Algebra Research
- Rings, Modules, and Algebras
- Advanced Algebra and Geometry
- Nonlinear Waves and Solitons
- Nuclear reactor physics and engineering
- Geological Studies and Exploration
- Matrix Theory and Algorithms
- Climate variability and models
- Graphite, nuclear technology, radiation studies
- Meteorological Phenomena and Simulations
- Commutative Algebra and Its Applications
- Arctic and Antarctic ice dynamics
- Cold Atom Physics and Bose-Einstein Condensates
- Nuclear Physics and Applications
- Radiation Detection and Scintillator Technologies
- Advanced Data Processing Techniques
- Economic and Technological Systems Analysis
- Atmospheric and Environmental Gas Dynamics
- Solar and Space Plasma Dynamics
- Advanced Algebra and Logic
- Geophysics and Gravity Measurements
- Nuclear Engineering Thermal-Hydraulics
St Petersburg University
2015-2024
Institute of Monitoring of Climatic and Ecological Systems
2016-2022
Kazan Federal University
2019
National Research Tomsk State University
2012-2018
Tomsk Polytechnic University
1972-2018
Universidade de São Paulo
2015-2017
Obninsk Institute for Nuclear Power Engineering
2015
National Research Nuclear University MEPhI
2015
The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such modulo isomorphism. Then describe degenerations and closures principal algebra series in under consideration. Finally, apply our results obtain analogous descriptions for subvarieties flexible, bicommutative algebras. In particular, rigid irreducible components these subvarieties.
We describe all rigid algebras and irreducible components in the variety of four dimensional Leibniz $\mathfrak{Leib}_4$ over $\mathbb{C}.$ In particular, we prove that Grunewald--O'Halloran conjecture is not valid Vergne for $\mathfrak{Leib}_4.$
We describe degenerations of four-dimensional Zinbiel and nilpotent Leibniz algebras over C. In particular, we all irreducible components in the corresponding varieties.
For some exact monoidal categories, we describe explicitly a connection between topological and algebraic definitions of the Lie bracket on extension algebra unit object. The definition, due to Schwede Hermann, involves loops in definition homotopy liftings as introduced by first author. As consequence our description, prove that indeed yields Gerstenhaber structure category setting, answering question Hermann. use proofs, generalize $A_{\infty}$-coderivation lifting techniques from bimodule...
We describe degenerations of four-dimensional binary Lie algebras, and five- six-dimensional nilpotent Malcev algebras over ℂ. In particular, we all irreducible components these varieties.
The main result of the paper is classification all (nonassociative) algebras level two, i.e. such that maximal chains nontrivial degenerations starting at them have length two. During this we obtain an estimation algebra via its generation type, dimension one generated subalgebra. Also describe and levels type $1$ with a square zero ideal codimension $1$.
Abstract We describe all degenerations of three-dimensional anticommutative algebras $\mathfrak{A}\mathfrak{c}\mathfrak{o}\mathfrak{m}_{3}$ and Leibniz $\mathfrak{L}\mathfrak{e}\mathfrak{i}\mathfrak{b}_{3}$ over $\mathbb{C}$ . In particular, we irreducible components rigid in the corresponding varieties.
Abstract We prove formulas of different types that allow us to calculate the Gerstenhaber bracket on Hochschild cohomology an algebra using some arbitrary projective bimodule resolution for it. Using one these formulas, we give a new short proof derived invariance structure cohomology. also Connes differential homology lead Batalin–Vilkovisky (BV) in case symmetric algebras. Finally, use obtained provide full description BV and, correspondingly, class
We consider the variety of Filippov ($n$-Lie) algebra structures on an $(n+1)$-dimensional vector space. The group $GL_n(K)$ acts it, and we study orbit closures with respect to Zariski topology. This leads definition degenerations. present some fundamental results such degenerations, including trace invariants necessary degeneration criteria. Finally, classify all in complex $n$-ary algebras.
The Hochschild cohomology algebra for a series of self-injective algebras the tree class $D_n$ is described in terms generators and relations. proof involves existing description minimal bimodule resolvent additive structure question.
Anticommutative Engel algebras of the first five degeneration levels are classified. All appearing in this classification nilpotent Malcev algebras.
In 1990 Kantor defined the conservative algebra $W(n)$ of all algebras (i.e. bilinear maps) on $n$-dimensional vector space. If $n>1$, then does not belong to any well-known class (such as associative, Lie, Jordan, or Leibniz algebras). We describe automorphisms, one-sided ideals, and idempotents $W(2).$ Also similar problems are solved for $W_2$ commutative 2-dimensional space $S_2$ with trace zero multiplication