Fred Goodman (Iowa), Cellularity and the basic construction.

Abstract:

I will discuss an approach to cellularity of "algebras with a Jones basic construction" such as the BMW, Brauer, partition, or Temperley--Lieb algebras. There was a mistake in the original paper on this subject and I will discuss the mistake and how to avoid it. The upshot is that the results of the original paper do not hold over the generic ground ring for each algebra but only over the ground ring with $\delta^{-1}$ adjoined, where $e_1^2 = \delta e_1$. However, Enyang and I have produced Murphy type bases for these algebras and these bases are valid over the generic ground ring.