1. Central ideals and Cartan invariants of symmetric algebras
- Author
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Héthelyi, László, Horváth, Erzsébet, Külshammer, Burkhard, and Murray, John
- Subjects
- *
ALGEBRA , *MATHEMATICAL analysis , *ALGEBRAIC fields , *MATHEMATICS - Abstract
Abstract: In this paper, we investigate certain ideals in the center of a symmetric algebra A over an algebraically closed field of characteristic . 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 , 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. [Copyright &y& Elsevier]
- Published
- 2005
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