Highest Weight Categories Arising from Khovanov's Diagram Algebra I: Cellularity

Abstract

This is the first of four articles studying some slight generalisations H n m of Khovanov's diagram algebra, as well as quasi-hereditary covers K n m of these algebras in the sense of Rouquier, and certain infinite dimensional limiting versions K ∞ m , K ±∞ 12 4.The algebra K Λ : a larger cellular algebra 19 5.The quasi-hereditary structure of K Λ 25 6.Further results 31 References 36