2023/03/01 by Li, Yanbo, Sun, Bowen
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2303.00358
In this note, we prove that an affine cellular algebra A is semisimple if and only if the scheme associated to A is reduced and 0-dimensional, and the bilinear forms with respect to all layers of A are isomorphisms. Moreover, if the ground ring is a perfect field, then A is semisimple if and only if it is separable. We also give a sufficient condition for an affine cellular algebra being Jacobson semisimple.