Skip Navigation

International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn039, 10 pages, doi:10.1093/imrn/rnn039 published on April 28, 2008
This Article
Right arrow Full Text (PDF)
Right arrow References
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
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Dobrovolska, G.
Right arrow Articles by Etingof, P.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

An Upper Bound for the Lower Central Series Quotients of a Free Associative Algebra

Galyna Dobrovolska

Pavel Etingof

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Correspondence: Correspondence to be sent to: galyna{at}mit.edu

Feigin and Shoikhet conjectured in [4], Feigin and Shoikhet, Mathematical Research Letters, 14,2007,781–95 that successive quotients Bm(An) of the lower central series filtration of a free associative algebra An have polynomial growth. In this paper we give a proof of this conjecture, using the structure of a representation of Wn, the Lie algebra of polynomial vector fields on Formula , on Bm(An) which was defined in [4]. Moreover, we show that the number of squares in a Young diagram D corresponding to an irreducible Wn-module in the Jordan–Hölder series of Bm(An) is bounded above by the integer Formula , which allows us to confirm the structure of B3(A3) conjectured in [4].


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.