Skip Navigation

Journal of the London Mathematical Society 2003 68(2):355-370; doi:10.1112/S0024610703004484
© 2003 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Bryant, R. M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

Free Lie Algebras and Adams Operations

R. M. Bryant

Department of Mathematics, UMIST PO Box 88, Manchester M60 1QD, bryant{at}umist.ac.uk

Received 15 February 2002. Revision received 21 January 2003.

Let G be a group and K a field. For any finite-dimensional KG-module V and any positive integer n, let Ln(V) denote the nth homogeneous component of the free Lie K-algebra generated by (a basis of) V. Then Ln(V) can be considered as a KG-module, called the nth Lie power of V. The paper is concerned with identifying this module up to isomorphism. A simple formula is obtained which expresses Ln(V) in terms of certain linear functions on the Green ring. When n is not divisible by the characteristic of K these linear functions are Adams operations. Some results are also obtained which clarify the relationship between Adams operations defined by means of exterior powers and symmetric powers and operations introduced by Benson. Some of these results are put into a more general setting in an appendix by Stephen Donkin.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.