408 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Novosibirsk State UniversityRU417 papers
- Siberian Branch of the Russian Academy of SciencesRU56 papers
- Russian Academy of SciencesRU50 papers
- University of LiègeBE36 papers
- Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza34 papers
- University of CalabriaIT32 papers
- Centre National de la Recherche ScientifiqueFR30 papers
- National Research Tomsk State UniversityRU28 papers
- Istituto Nazionale di Fisica NucleareIT23 papers
- Tomsk State Pedagogical UniversityRU22 papers
- University of Illinois Urbana-ChampaignUS21 papers
- Lomonosov Moscow State UniversityRU18 papers
83 papers · 1 filter
Rota-Baxter operators on the simple Jordan algebra of matrices of order two
Vsevolod Gubarev, Alexander Panasenko
We describe all Rota-Baxter operators of any weight on the space of matrices from considered under the product and usually denoted as $M_2(F)^{(+)…
Rota-Baxter operators of nonzero weight on the split Cayley-Dickson algebra
A. S. Panasenko
We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obta…
On the Dong Property for a binary quadratic operad
P. S. Kolesnikov, B. K. Sartayev
The classical Dong Lemma for distributions over a Lie algebra lies in the foundation of vertex algebras theory. In this paper, we find necessary and sufficient condition for a vari…
Hochschild cohomology of the universal associative conformal envelope of the Virasoro Lie conformal algebra with coefficients in all finite modules
Hassan Alhussein, Pavel Kolesnikov, Viktor Lopatkin
In this paper, we find the Hochschild cohomology groups of the universal associative conformal envelope of the Virasoro Lie conformal algebra with respect to associative loc…
Rota-Baxter operators of weight zero on the matrix algebra of order three without unit in kernel
Vsevolod Gubarev
We describe all Rota-Baxter operators of weight zero on the matrix algebra over a quadratically closed field of characteristic not 2 or 3 such that . Th…
On polynomial equations over split octonions
Artem Lopatin, Alexander N. Rybalov
Working over the split octonions over an algebraically closed field, we solve all polynomial equations in which all the coefficients but the constant term are scalar. As a conseque…
Differential envelopes of Novikov conformal algebras
P. S. Kolesnikov, A. A. Nesterenko
A Novikov conformal algebra is a conformal algebra such that its coefficient algebra is right-symmetric and left commutative (i.e., it is an ``ordinary'' Novikov algebra). We prove…
On the pre-commutative envelopes of commutative algebras
H. Alhussein, P. Kolesnikov
We prove that every nilpotent commutative algebra can be embedded into a pre-commutative (Zinbiel) algebra with respect to the anti-commutator operation. For finite-dimensional alg…
Rota-Baxter operators of weight zero on upper-triangular matrices of order three
Vsevolod Gubarev
We describe all Rota-Baxter operators of weight zero on the algebra of upper-triangular matrices of order three over a field of characteristic 0. For this, we apply th…
Burde's series of simple pre-Lie algebras
Vsevolod Gubarev
We describe automorphisms, derivations, and Rota -- Baxter operators on the series of simple pre-Lie algebras found by D. Burde in 1998.
On -generated axial algebras of Jordan type
Ravil Bildanov, Ilya Gorshkov
Axial algebras of Jordan type are a special type of commutative non-associative algebras. They are generated by idempotents whose adjoint operators have the minimal polynomial…
Nonunital decompositions of the matrix algebra of order three
Vsevolod Gubarev
All decompositions of into a direct vector-space sum of two subalgebras such that none of the subalgebras contains the identity matrix are classified. Thus, the c…
Generalized sharped cubic form and split spin factor algebra
Vsevolod Gubarev, Farukh Mashurov, Alexander Panasenko
There is a well-known construction of a Jordan algebra via a sharped cubic form. We introduce a generalized sharped cubic form and prove that the split spin factor algebra is induc…
On Pre-Novikov Algebras and Derived Zinbiel Variety
Pavel Kolesnikov, Farukh Mashurov, Bauyrzhan Sartayev
For a non-associative algebra with a derivation , its derived algebra is the same space equipped with new operations , , $a,b\i…
Hochschild cohomology of the Weyl conformal algebra with coefficients in finite modules
H. Alhussein, P. Kolesnikov
In this work we find Hochschild cohomology groups of the Weyl associative conformal algebra with coefficients in all finite modules. The Weyl conformal algebra is the universal ass…
On radicals of Novikov algebras
A. S. Panasenko
We show that in a prime nonassociative Novikov algebra every nonzero ideal is non-associative. We prove that Baer (and Andrunakievich) radical and left quasiregular radical coincid…
Separating G_2-invariants of several octonions
Artem Lopatin, Alexandr N. Zubkov
We describe separating G_2-invariants of several copies of the algebra of octonions over an algebraically closed field of characteristic two. We also obtain a minimal separating an…
Classification of G_2-orbits for pairs of octonions
Artem Lopatin, Alexandr N. Zubkov
Over an algebraically closed field, we described a minimal set of representatives for G_2-orbits on the set of pairs of octonions.
Semiprime Novikov Algebras
A. S. Panasenko
We study prime and semiprime Novikov algebras. We prove that prime nonassociative Novikov algebra has zero nucleus and center. It is well known that an ideal of an alternative (sem…
Noncommutative Novikov algebras
P. Kolesnikov, B. Sartayev
The class of Novikov algebras is a popular object of study among classical nonassociative algebras. The generic example of a Novikov algebra may be obtained from a differential ass…
Quasi-definite axial algebras of Jordan type half
Ilya Gorshkov, Vsevolod Gubarev
Axial algebras are commutative nonassociative algebras generated by a finite set of primitive idempotents which action on an algebra is semisimple, and the fusion laws on the produ…
Universal enveloping algebra of a pair of compatible Lie brackets
Vsevolod Gubarev
Applying the Poincare-Birkhoff-Witt property and the Groebner-Shirshov bases technique, we find the linear basis of the associative universal enveloping algebra in the sense of V.…
On the special identities of Gelfand--Dorfman algebras
P. S. Kolesnikov, B. K. Sartayev
In this paper, we prove that the class of all special Gelfand--Dorfman algebras (GD-algebras) is closed with respect to homomorphisms and thus forms a variety. We also prove that e…
Double Lie algebras of a nonzero weight
Maxim Goncharov, Vsevolod Gubarev
We introduce the notion of -double Lie algebra, which coincides with usual double Lie algebra when . We state that every -double Lie algebra for provides the s…