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tube algebra

Proceedings of the Edinburgh Mathematical Society (1)

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A Few Remarks on the Tube Algebra of a Monoidal Category
Part of
Sergey Neshveyev, Makoto Yamashita
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 61 / Issue 3 / August 2018

Published online by Cambridge University Press:

08 May 2018, pp. 735-758
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We prove two results on the tube algebras of rigid C*-tensor categories. The first is that the tube algebra of the representation category of a compact quantum group G is a full corner of the Drinfeld double of G. As an application, we obtain some information on the structure of the tube algebras of the Temperley–Lieb categories 𝒯ℒ(d) for d > 2. The second result is that the tube algebras of weakly Morita equivalent C*-tensor categories are strongly Morita equivalent. The corresponding linking algebra is described as the tube algebra of the 2-category defining the Morita context.