Hethelyi, Laszlo and Horvath, Erzsebet and Kulshammer, Burkhard and Murray, John
Central Ideals and Cartan Invariants
of Symmetric Algebras.
Journal of Alegbra, 293 (1).
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.
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