Cellularity and Jones basic construction

Cellularity and Jones basic construction

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 pa...

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Bibliographic Details
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
Description
Summary: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.

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