4 papers
A vanishing criterion for Lie elements in a free Novikov algebra
F. A. Mashurov, B. K. Sartayev
Every Novikov algebra is Lie-admissible: the commutator turns it into a Lie algebra. We give a finite criterion for a multilinear element of the free Novikov algebra to belong to t…
A polynomial criterion for Jordan elements in a free associative algebra
F. Mashurov, B. Sartayev
Let be a free associative algebra over a field of characteristic zero, and let be the Jordan subalgebra of generated by and . For every $…
Free Novikov-Zinbiel algebra
A. Dauletiyarova, F. Mashurov, B. Sartayev
Let be a commutative-associative algebra with an invertible derivation , and put . We study the operations \begin{equation*} x\succ y=R(x)y,\qquad x\prec y=xD(y),…
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…