Frobenius algebras, triangulations and tensor categories

Many aspects of algebra and representation theory can be generalized from the category of vector spaces to more general categories. In fact, super-mathematics is based on such a generalization of standard mathematical constructions to the category of super-vector spaces. It has recently been realized that conformal field theories in two dimensions, i.e. the quantum field theories on the worldsheet of a string, can be understood as the theory of (Frobenius-)algebras in certain categories, so-called modular tensor categories.

Christoph Schweigert

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