Tube algebra of group-type subfactors
Dietmar Bisch, Paramita Das, Shamindra Kumar Ghosh, Narayan Rakshit
TL;DR
This paper analyzes the structure of the tube algebra associated with certain subfactors, revealing its decomposition into twisted representation categories linked to conjugacy classes and cocycle obstructions.
Contribution
It provides a detailed description of the tube algebra and its representations for diagonal and Bisch-Haagerup subfactors, incorporating scalar 3-cocycle obstructions.
Findings
Tube algebra decomposes into twisted representation categories
Categories are additively equivalent to products over conjugacy classes
Incorporates scalar 3-cocycle obstructions into the analysis
Abstract
We describe the tube algebra and its representations in the cases of diagonal and Bisch-Haagerup subfactors possibly with a scalar 3-cocycle obstruction. We show that these categories are additively equivalent to the direct product over conjugacy classes of representation category of a centralizer subgroup (corresponding to the conjugacy class) twisted by a scalar 2-cocycle obtained from the 3-cocycle obstruction.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology