Cellular Algebras: Inflations and Morita Equivalences

A characteristic free approach to Brauer algebras

“…We have introduced this concept for general cellular algebras in [KX2] and shown (theorem 4.1 in [KX2]) that actually an algebra is cellular if and only if it is such an iterated inflation. Special cases of inflations can be found in the papers of Graham and Lehrer [GL], Hanlon and Wales [HW1] and even in the early studies of Brown [Brow1,Brow2,Brow3], who considered 'generalised matrix algebras' which coincide in his case with our inflations.…”

“…In [KX2] (theorem 4.1) we have shown that an algebra is cellular if and only if it can be written as an iterated inflation of copies of full matrix algebras. Moreover ( [KX2], proposition 3.4) an iterated inflation of cellular algebras always is cellular again.…”

“…Moreover ( [KX2], proposition 3.4) an iterated inflation of cellular algebras always is cellular again.…”

Cellular Bases for Algebras with a Jones Basic Construction

“…When it is necessary to identify the algebra we are working with, we will write α A λ instead of α λ . The importance of the maps α λ for the structure of cellular algebras was stressed by König and Xi [23,24].…”

The representation theory of cyclotomic Temperley-Lieb algebras

“…According to a general construction in [11], there is a bilinear form φ (n,k) from V (n, k) ⊗ R V (n, k) to G m,n−2k such that the product can be written as…”