Cellularity and Jones basic construction

• Main Author: Graber, John Eric
• Other Authors: Goodman, Frederick M.
• Format: Others
• Language: English
• Published: University of Iowa 2009
• Subjects: Basic Construction; Cellularity; Cyclotomic BMW Algebra; Cyclotomic Hecke Algebra; Jones; Mathematics
• Online Access: https://ir.uiowa.edu/etd/292; https://ir.uiowa.edu/cgi/viewcontent.cgi?article=1477&context=etd

This thesis establishes a framework for cellularity of algebras related to the Jones basic construction. The framework allows a uniform proof of cellularity of Brauer algebras, BMW algebras, walled Brauer algebras, partition algebras, and others. In this setting, the cellular bases are labeled by paths on certain branching diagrams rather than by tangles. Moreover, for this class of algebras, the cellular structures are compatible with restriction and induction of modules.