Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



On a class of finitary Lie algebras characterized through derivations

Authors: Matej Brešar and Antonio Fernández López
Journal: Proc. Amer. Math. Soc. 138 (2010), 4161-4166
MSC (2010): Primary 17B40, 17B65; Secondary 16W10
Published electronically: August 10, 2010
MathSciNet review: 2680042
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ L$ be an infinite-dimensional simple Lie algebra over a field of characteristic 0. Then there exist a derivation $ d$ on $ L$ and $ n\ge 2$ such that $ d^n$ is a nonzero finite rank map if and only if $ L$ is finitary and contains a nonzero finite-dimensional abelian inner ideal. This is a partial statement of our main theorem. As auxiliary results needed for the proof we establish some properties of derivations in general nonassociative algebras.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 17B40, 17B65, 16W10

Retrieve articles in all journals with MSC (2010): 17B40, 17B65, 16W10

Additional Information

Matej Brešar
Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadravska ulica 19, SI-1000 Ljubljana, Slovenia – and – Faculty of Natural Sciences and Mathematics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia

Antonio Fernández López
Affiliation: Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071 Malaga, Spain

Keywords: Derivation, finite rank, nonassociative algebra, simple Lie algebra, finitary Lie algebra, inner ideal
Received by editor(s): October 27, 2009
Published electronically: August 10, 2010
Additional Notes: The first author was supported by the Slovenian Research Agency (Program No. P1-0288).
The second author was supported by the MEC and Fondos FEDER, MTM2007-61978
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2010 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia