5 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),…
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 , i.e. an associative algebra satisfying equipped with a derivation . We investi…