5 papers
On the free metabelian transposed Poisson and F-manifold algebras
K. Abdukhalikov, B. K. Sartayev
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…
Shift associative algebras
Hani Abdelwahab, Ivan Kaygorodov, Bauyrzhan Sartayev
We present a comprehensive study of algebras satisfying the identity named as shift associative algebras. Our research shows that these algebras are related to many…
Basis of the free noncommutative Novikov algebra
B. K. Sartayev
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 obtai…
Free special Gelfand-Dorfman algebra
V. Gubarev, B. K. Sartayev
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…
Novikov dialgebras and perm algebras
F. Mashurov, B. K. Sartayev
In this paper, we consider Perm algebra with the derivation . The algebra itself is equipped with the new operation . We construct a linear basis of the free…