Cellular algebras. (English) Zbl 0853.20029

The authors define a class of associative algebras (“cellular”) by means of multiplicative properties of a basis, show that they have cell representations whose structure depends on certain invariant bilinear forms, and then obtain a general description of their irreducible representations and block theory as well as criteria for semisimplicity. These concepts are used to discuss the Brauer centraliser algebras, the Ariki-Koike algebras and the Temperley-Lieb and Jones algebras.


20G05 Representation theory for linear algebraic groups
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
20C30 Representations of finite symmetric groups
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