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Hethelyi, Laszlo, Horvath, Erzsebet, Kulshammer, Burkhard and Murray, John (2005) Central Ideals and Cartan Invariants of Symmetric Algebras. Journal of Alegbra, 293 (1). pp. 243-260. ISSN 0021-8693
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Abstract
In this paper, we investigate certain ideals in the center of a symmetric algebra
A over an algebraically closed eld of characteristic p > 0. These ideals include the
Higman ideal and the Reynolds ideal. They are closely related to the p-power map on
A. We generalize some results concerning these ideals from group algebras to symmetric
algebras, and we obtain some new results as well. In case p = 2, these ideals detect odd
diagonal entries in the Cartan matrix of A. In a sequel to this paper, we will apply our
results to group algebras.
| Item Type: | Article |
|---|---|
| Keywords: | Central Ideals; Cartan Invariants; Symmetric Algebras; |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 2034 |
| Depositing User: | Dr. John Murray |
| Date Deposited: | 06 Jul 2010 14:55 |
| Journal or Publication Title: | Journal of Alegbra |
| Publisher: | Elsevier |
| Refereed: | No |
| Related URLs: | |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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