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

Richard, Lionel; Silvestrov, Sergei

doi:10.1007/978-3-540-85332-9_22

Lionel Richard⁵ &
Sergei Silvestrov

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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.

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References

Hartwig, J.T., Larsson, D., Silvestrov, S.D.: Deformations of Lie algebras using σ-derivations. J. Algebra 295 (2006), 314–361
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Authors and Affiliations

School of Mathematics of the University of Edinburgh and Maxwell Institute for Mathematical Sciences, JCMB—King's Buildings, Edinburgh, EH9 3JZ, UK
Lionel Richard

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Lionel Richard
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Sergei Silvestrov
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Editors and Affiliations

Centre for Mathematical Sciences, Division of Mathematics, Lund Institute of Technology, Lund University, Box 118, Lund, 221 00, Sweden
Sergei Silvestrov
Department of Mathematics, Tallinn University of Technology, Ehitajate tee 5, Tallinn, 19086, Estonia
Eugen Paal
Institute of Pure Mathematics, University of Tartu, J. Liivi 2, Tartu, 50409, Estonia
Viktor Abramov
Department of Mathematical Sciences, Mathematical Sciences Chalmers University of Technology and Göteborg University, Göteborg, 412 96, Sweden
Alexander Stolin

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Richard, L., Silvestrov, S. (2009). A Note on Quasi-Lie and Hom-Lie Structures of σ-Derivations of C=[Z ^±1₁ ,…,Z ^±1_n ]. In: Silvestrov, S., Paal, E., Abramov, V., Stolin, A. (eds) Generalized Lie Theory in Mathematics, Physics and Beyond. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85332-9_22

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DOI: https://doi.org/10.1007/978-3-540-85332-9_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85331-2
Online ISBN: 978-3-540-85332-9
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A Note on Quasi-Lie and Hom-Lie Structures of σ-Derivations of C=[Z ±11 ,…,Z ±1n ]