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On planar algebras arising from hypergroups

โœ Scribed by R.M. Green

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
239 KB
Volume
263
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

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 .

๐Ÿ“œ SIMILAR VOLUMES

Fourier algebras on locally compact hype
Fourier algebras on locally compact hypergroups
โœ M. Lashkarizadeh Bami; M. Pourgholamhossein; H. Samea ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 153 KB

## Abstract In the present paper we introduce a new definition for the Fourier space __A__ (__K__) of a locally compact Hausdorff hypergroup __K__ and prove that it is a Banach subspace of __B__ (__K__). This definition coincides with that of Amini and Medghalchi in the case where __K__ is a tensor

Semicanonical Bases Arising From Envelop
Semicanonical Bases Arising From Enveloping Algebras
โœ G. Lusztig ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 153 KB

Let U + be the plus part of the enveloping algebra of a Kac Moody Lie algebra g with a symmetric Cartan datum. In [L1] we have defined a canonical basis of U + under the assumption that the Cartan datum is of finite type; this was later generalized to Cartan data of possibly infinite type in [K, L3]