Classification of module categories for \(SO (3)_{2m} \). (English) Zbl 07415143
Summary: The main goal of this paper is to classify \(\ast \)-module categories for the \(S O ( 3 )_{2 m}\) modular tensor category. This is done by classifying \(S O ( 3 )_{2 m}\) nimrep graphs and cell systems, and in the process we also classify the \(S O(3)\) modular invariants. There are module categories of type \(\mathcal{A}\), \(\mathcal{E}\) and their conjugates, but there are no orbifold (or type \(\mathcal{D} )\) module categories. We present a construction of a subfactor with principal graph given by the fusion rules of the fundamental generator of the \(S O ( 3 )_{2 m}\) modular category. We also introduce a Frobenius algebra \(A\) which is an \(S O(3)\) generalisation of (higher) preprojective algebras, and derive a finite resolution of \(A\) as a left \(A\)-module along with its Hilbert series.
MSC:
| 81Txx | Quantum field theory; related classical field theories |
| 46Lxx | Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.) |
| 17Bxx | Lie algebras and Lie superalgebras |
Keywords:
\(\operatorname{SO}(3)\); module categories; modular tensor categories; subfactors; quantum subgroupsReferences:
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