Central Ideals and Cartan Invariants of Symmetric Algebras

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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:	http://www.sciencedirect.com/science/jou...
URI:	https://mural.maynoothuniversity.ie/id/eprint/2034
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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Central Ideals and Cartan Invariants of Symmetric Algebras

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