A Note on Quasi-Lie and Hom-Lie Structures of σ-Derivations of C=[Z 1 ±1,…,Z n ±1 ]

Lionel Richard () and Sergei Silvestrov ()
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Lionel Richard: JCMB—King's Buildings, School of Mathematics of the University of Edinburgh and Maxwell Institute for Mathematical Sciences
Sergei Silvestrov: Lund Institute of Technology, Lund University, Centre for Mathematical Sciences, Division of Mathematics

Chapter 22 in Generalized Lie Theory in Mathematics, Physics and Beyond, 2009, pp 257-262 from Springer

Abstract: In a previous paper we studied the properties of the bracket defined by Hartwig, Larsson and the second author in (J. Algebra 295, 2006) on σ-derivations of Laurent polynomials in one variable. Here we consider the case of several variables, and emphasize on the question of when this bracket defines a hom-Lie structure rather than a quasi-Lie one.

Date: 2009
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DOI: 10.1007/978-3-540-85332-9_22

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