Symmetries of subfactors

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A subfactor is a mathematical object that encodes "quantum" symmetries which may be thought of as generalisations of group symmetries. This project will study subfactors and classify families of subfactor symmetries which include the exotic subfactors of small index. It will also develop computational tools for analysing and cataloguing these symmetries. This project contributes to the development of operator algebra theory, and the new mathematical fields of quantum algebra and quantum topology; it also has applications to physical models.