Is there a vector house whose size is the golden ratio? after all not--the golden ratio isn't really an integer! yet this may ensue for generalizations of vector spaces--objects of a tensor classification. the speculation of tensor different types is a comparatively new box of arithmetic that generalizes the idea of workforce representations. It has deep connections with many different fields, together with illustration conception, Hopf algebras, operator algebras, low-dimensional topology (in specific, knot theory), homotopy conception, quantum mechanics and box conception, quantum computation, concept of factors, and so forth. This publication supplies a scientific advent to this conception and a evaluate of its functions. whereas giving an in depth review of normal tensor different types, it focuses particularly at the idea of finite tensor different types and fusion different types (in specific, braided and modular ones), and discusses the most effects approximately them with proofs. particularly, it exhibits how the most houses of finite-dimensional Hopf algebras should be derived from the speculation of tensor different types. Many vital effects are awarded as a chain of routines, which makes the e-book worthwhile for college kids and compatible for graduate classes. Many functions, connections to different components, extra effects, and references are mentioned on the finish of every bankruptcy.

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