Cohomological stratification of diagram algebras.
Combining the notions of cellular and stratified algebras the authors define a class of algebras which they call `cellularly stratified algebras'. In the definition the authors impose some extra conditions in addition to the cellular structure. These conditions strongly resemble properties of regular \(\mathcal D\)-classes in semigroups and ensure that the obtained algebra is also stratified in the sense of Cline, Parshall and Scott. The class of cellularly stratified algebras is shown to include many diagram algebras, in particular, Brauer algebras, Birman-Murakami-Wenzl algebras and partition algebras. The authors propose various structural characterizations for cellularly stratified algebras and study certain induction functors from layers of the stratification. The first application establishes tools for comparison of decomposition numbers for a cellularly stratified algebra and components of the stratification. The second application provides equivalences between certain categories of modules filtered by various structural modules. In the last section a Schur-Weyl duality for cellularly stratified algebras is presented.
scientific article; zbMATH DE number 5721504
scientific article