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Central ideals and Cartan invariants of symmetric algebras
- Source :
-
Journal of Algebra . Nov2005, Vol. 293 Issue 1, p243-260. 18p. - Publication Year :
- 2005
-
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]
- Subjects :
- *ALGEBRA
*MATHEMATICAL analysis
*ALGEBRAIC fields
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 293
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 18732185
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2005.01.052