Cellular algebra

Summary

A cellular algebra is an associative algebra with a special basis, the cellular basis. This basis is compatible with an anti-involution and with a partial order on its labels. The notion was introduced by Graham and Lehrer. The basis produces cell modules, which play the role of the Specht modules of the symmetric group. The simple modules come out of the cell modules in a uniform way. Hecke algebras of type $A$, Temperley–Lieb algebras and Brauer algebras are cellular.