Radicals of symmetric cellular algebras

Volume 133 / 2013

Yanbo Li 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.

Authors

  • Yanbo LiSchool of Mathematics and Statistics
    Northeastern University at Qinhuangdao
    Qinhuangdao, 066004, P.R. China
    e-mail

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