On Planar Algebras Arising from Hypergroups
نویسنده
چکیده
Let A be an associative algebra with identity and with trace. We study the family of planar algebras on 1-boxes that arise from A in the work of Jones, but with the added assumption that the labels on the 1-boxes come from a discrete hypergroup in the sense of Sunder. This construction equips the algebra P A n with a canonical basis, B A n , which turns out to be a \tabular" basis. We examine special cases of this construction to exhibit a close connection between such bases and Kazhdan{Lusztig bases of Hecke algebras of types A, B, H or I.
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