Sandwich cellularity and a version of cell theory

Abstract

We explain how the theory of sandwich cellular algebras can be seen as a version of cell theory for algebras. We apply this theory to many examples such as Hecke algebras, and various monoid and diagram algebras.

33 pages, many figures, to appear in Rocky Mountain J. Math., comments welcome

References in corpus (16)

• Idempotents of Hecke algebras of type A
• Hecke algebras of finite type are cellular
• Super $q$-Howe duality and web categories
• The Blanchet-Khovanov algebras
• Integral presentations of quantum lattice Heisenberg algebras
• Cellular structures using ${\text{U}}_q$-tilting modules
• Finitary birepresentations of finitary bicategories
• Semisimplicity of Hecke and (walled) Brauer algebras
• The Modular Temperley-Lieb Algebra
• Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types
• Cellularity for weighted KLRW algebras of types $B$, $A^{(2)}$, $D^{(2)}$
• Relative cellular algebras
• Cellularity and subdivision of KLR and weighted KLRW algebras
• Monoidal categories, representation gap and cryptography
• HOMFLYPT homology for links in handlebodies via type A Soergel bimodules
• Cellularity of the p-Canonical Basis for Symmetric Groups

Cited by in corpus (4)

• Uncoiled affine Temperley-Lieb algebras and their Wenzl-Jones projectors
• Growth problems in diagram categories
• Cellularity of KLR and weighted KLRW algebras via crystals
• On rank one 2-representations of web categories