Tensor categories

Is there a vector space whose dimension is the golden ratio? Of course not-the golden ratio is not an integer! But this can happen for generalizations of vector spaces-objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This bo