Radicals of symmetric cellular algebras
Volume 133 / 2013
Colloquium Mathematicum 133 (2013), 67-83
MSC: 16G30, 16N20.
DOI: 10.4064/cm133-1-5
Abstract
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.
