Central Ideals and Cartan Invariants of Symmetric Algebras

Hethelyi, Laszlo and Horvath, Erzsebet and 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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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

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