Cellularity and the Jones basic construction
We establish a framework for cellularity of algebras related to the Jones basic construction. Our framework allows a uniform proof of cellularity of Brauer algebras, ordinary and cyclotomic BMW algebras, walled Brauer algebras, partition algebras, and others. Our cellular bases are labeled by paths on certain branching diagrams rather than by tangles. Moreover, for the class of algebras that we study, we show that the cellular structures are compatible with restriction and induction of modules. Applied to cyclotomic BMW algebras, our method allows a new a shorter proof of the finite spanning result and isomorphism with cyclotomic Kauffman tangle algebras.
The performance of polymer:fullerene solar cells is strongly affected by the active layer morphology and polymer microstructure. In this Perspective, we review ongoing research on how structural factors influence the photogeneration and collection of charge carriers as well as charge carrier recombination and the related open-circuit voltage. We aim to highlight unexplored research opportunities and provide some guidelines for the synthesis of new conjugated polymers for high-efficiency solar cells.