Inner and Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

Abstract

Abstract Let L m, c be the free metabelian nilpotent of class c Lie algebra of rank m over a field K of characteristic 0. We describe the groups of inner and outer automorphisms of L m, c . To obtain this result, we first describe the groups of inner and continuous outer automorphisms of the completion with respect to the formal power series topology of the free metabelian Lie algebra F m of rank m. Key Words: Baker-Campbell-Hausdorff formulaFree metabelian Lie algebrasInner automorphismsOuter automorphisms2010 Mathematics Subject Classification: 17B0117B3017B40 ACKNOWLEDGMENTS The research of the second named author was partially supported by the Council of Higher Education (YÖK) in Turkey. He is also very grateful to the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences for the creative atmosphere and the warm hospitality during his visit when most of this project was carried out. Notes Communicated by I. Shestakov.

Locations

• arXiv (Cornell University) - View - PDF
• Communications in Algebra - View