Quasi-Lie structure of twisted derivations of Laurent polynomials
  Hartwig, Larsson and the second author in [J. Algebra, 2005] defined a bracket on sigma-derivations of a commutative algebra. We show that this bracket preserves inner derivations, and based on this obtain some structural results on sigma-derivations on Laurent polynomials in one variable. 
Lionel Richard, Sergei Silvestrov