6 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 the Jordan subalgebra of the free associative algebra $\Q\langle X\rangle$ generated by and under . We give a polynomial criterion for…
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),…
Nonsymmetric versions of binary quadratic operads
F. A. Mashurov, B. K. Sartayev
In this paper, we study the white Manin product of the associative operad $\As$ with a binary quadratic operad $\Var$. We introduce the notion of a nonsymmetric version of $\Var$ a…
Identities in differential perm algebras
F. A. Mashurov, B. K. Sartayev
Let be a differential perm algebra over a field of characteristic zero, i.e. an associative algebra satisfying and equipped with a derivation . We st…
Metabelian Lie and perm algebras
F. A. Mashurov, B. K. Sartayev
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 per…