Identities with a single skew derivation

In this chapter we consider the skew-primitive polynomials of the free character Hopf algebra to be quantum Lie operations. We discuss linearization and specialization processes and criteria for a polynomial to be classified as a quantum Lie operation. We also classify multilinear quantum Lie operations in two, three, and four variables.

Algebra of Skew-Primitive Elements

An Existence Condition for Multilinear Quantum Operations

Identities with Skew Derivations

Actions of pointed hopf algebras on prime algebras

In this paper we investigate algebraic dependencies between skew derivations of a prime ring mainly in the case when they commute with basic automorphisms; we also consider a Hopf algebra defining by the skew derivations and using its terms we discuss the problem about algebraic dependencies in general situation.

A.Z. Popov

Papers

Skew derivations of prime rings