Quasi-Lie structure of σ-derivations of C[t±1]

Abstract

Hartwig, Larsson and Silvestrov in [J.T. Hartwig, D. Larsson, S.D. Silvestrov, Deformations of Lie algebras using σ -derivations, J. Algebra 295 (2) (2006) 314-361] defined a bracket on σ -derivations of a commutative algebra. We show that this bracket preserves inner derivations, and based on this obtain structural results providing new insights into σ -derivations on Laurent polynomials in one variable.