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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.

MSC:
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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