A FEW REMARKS ON THE TUBE ALGEBRA OF A MONOIDAL CATEGORY

作者：Neshveyev Sergey; Yamashita Makoto^*

来源：Proceedings of the Edinburgh Mathematical Society, 2018, 61(3): 735-758.

DOI：10.1017/S0013091517000426

• C*-tensor category
• tube algebra
• Morita equivalence

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 T L(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.

• 出版日期2018-8