Projective cell modules of Frobenius cellular algebras

TL;DR

This paper characterizes when simple cell modules of Frobenius cellular algebras are projective, extending known results from symmetric cases and exploring dual bases conditions.

Contribution

It provides a necessary and sufficient condition for projectivity of simple cell modules in Frobenius cellular algebras, generalizing symmetric algebra results.

Findings

Characterization of projective simple cell modules

Condition involving dual bases in cellular algebras

Extension of symmetric case results to Frobenius case

Abstract

For a finite dimensional Frobenius cellular algebra, a sufficient and necessary condition for a simple cell module to be projective is given. A special case that dual bases of the cellular basis satisfying a certain condition is also considered. The result is similar to that in symmetric case.