Symmetry via braiding, diagrammatics and cellularity

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Symmetry is a basic organising tool for humans to understand their environment. Invariants are the mathematical embodiment of symmetry, and their study is as ancient as thought itself. This project aims to use the tools of braided tensor categories and cellular structure, to analyse the invariants occurring in several fundamental areas of mathematics, particularly relating to physics. The endomorphism algebras in certain tensor categories, particularly those for quantised superalgebras, will be realised as diagram algebras, and analysed using cellular theory. The intended output include criteria for semisimplicity, a new theory of diagram algebras, and decomposition theory which are expected to permit the determination of multiplicities of composition factors.