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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-1-5,
author = {Yanbo Li},
title = {Radicals of symmetric cellular algebras},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {67-83},
zbl = {1291.20004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-1-5}
}
Yanbo Li. Radicals of symmetric cellular algebras. Colloquium Mathematicae, Tome 131 (2013) pp. 67-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-1-5/