Vol. 107, No. 1, 1983

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Some Poincaré series related to identities of 2 × 2 matrices

Patrick Ronald Halpin

Vol. 107 (1983), No. 1, 107–115
Abstract

A partial solution to a problem of Procesi has recently been given by Formanek, Halpin, Li by determining the Poincaré series of the ideal of two variable identities of M2(k). Two related results are obtained in this article.

A weak identity of Mn(k) is a polynomial which vanishes identically on sln, the subspace of Mn(k) of matrices of trace zero. We show that the Poincaré series of the ideal of two variable weak identities of M2(k) is rational. In addition it is shown that the ideal of identities of upper triangular 2 × 2 matrices in an arbitrary finite number of variables has a rational Poincaré series. As an application we are able to determine this ideal precisely.

Mathematical Subject Classification 2000
Primary: 16A42, 16A42
Secondary: 18F25
Milestones
Received: 24 August 1981
Published: 1 July 1983
Authors
Patrick Ronald Halpin