Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Sartayev, B. K."'
Autor:
Abdukhalikov, K., Sartayev, B. K.
In this paper, we consider free transposed Poisson algebra and free F-manifold algebra with an additional metabelian identity. We construct a linear basis for both free metabelian transposed Poisson algebra and free metabelian F-manifold algebra.
Externí odkaz:
http://arxiv.org/abs/2408.05512
Publikováno v:
Communications in Mathematics, Volume 33 (2025), Issue 3 (Special issue: European Non-Associative Algebra Seminar) (May 9, 2024) cm:12877
In this paper, we consider Lie-admissible algebras, which are free Novikov and free Lie-admissible algebras with an additional metabelian identity. We construct a linear basis for both free metabelian Novikov and free metabelian Lie-admissible algebr
Externí odkaz:
http://arxiv.org/abs/2401.06993
Autor:
Kunanbayev, A., Sartayev, B. K.
In this paper, we describe the defining identities of a variety of binary perm algebras, which is a subvariety of the variety of alternative algebras. In addition, we construct a basis of the free binary perm algebra and find a complete list of ident
Externí odkaz:
http://arxiv.org/abs/2309.09503
Autor:
Sartayev, B. K.
Publikováno v:
Communications in Mathematics, Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024") (October 10, 2023) cm:11346
It is shown that the variety of transposed Poisson algebras coincides with the variety of Gelfand-Dorfman algebras in which the Novikov multiplication is commutative. The Gr\"obner-Shirshov basis for the transposed Poisson operad is calculated up to
Externí odkaz:
http://arxiv.org/abs/2305.12869
Autor:
Sartayev, B. K.
As it is known, the defining identities of a free Novikov algebra can be obtained from a commutative algebra with a derivation. In this paper, we consider a class of algebras obtained from the class of associative algebras with a derivation that gene
Externí odkaz:
http://arxiv.org/abs/2305.09985
Autor:
Gubarev, V., Sartayev, B. K.
A Gelfand-Dorfman algebra is called special if it can be embedded into a differential Poisson algebra. We find a new basis of the free Novikov algebra. With its help, we construct the monomial basis of the free special Gelfand-Dorfman algebra.
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Externí odkaz:
http://arxiv.org/abs/2208.10147
Autor:
Mashurov, F., Sartayev, B. K.
In this paper, we consider Perm algebra with the derivation $d$. The algebra itself is equipped with the new operation $a\succ b = d(a) b$. We construct a linear basis of the free Novikov dialgebra in terms of new operations. Also, we prove that the
Externí odkaz:
http://arxiv.org/abs/2206.12810
Autor:
Mashurov, F. A., Sartayev, B. K.
It is well known that any Lie algebra can be embedded into an associative algebra. We prove that any metabelian Lie algebra can be embedded into an algebra in the subvariety of perm algebras, i.e., associative algebras with the identity $abc-acb =0$.
Externí odkaz:
http://arxiv.org/abs/2110.06032
Autor:
Kolesnikov, P. S., Sartayev, B. K.
Given an associative algebra satisfying the left commutativity identity $abc=bac$ (Perm-algebra) with a derivation $d$, the new operation $a\circ b = a d(b)$ is left-symmetric (pre-Lie). We derive necessary and sufficient conditions for a left-symmet
Externí odkaz:
http://arxiv.org/abs/2106.00367
Autor:
Kolesnikov, P. S., Sartayev, B. K.
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 every 2-dimensional GD-algebra is special. For the latter, we give a te
Externí odkaz:
http://arxiv.org/abs/2105.13815