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Radicals of symmetric cellular algebras

Yanbo Li (2013)

Colloquium Mathematicae

For a symmetric cellular algebra, we study properties of the dual basis of a cellular basis first. Then a nilpotent ideal is constructed. The ideal connects the radicals of cell modules with the radical of the algebra. It also yields some information on the dimensions of simple modules. As a by-product, we obtain some equivalent conditions for a finite-dimensional symmetric cellular algebra to be semisimple.

Range inclusion results for derivations on noncommutative Banach algebras

Volker Runde (1993)

Studia Mathematica

Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes a result...

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