Is there a vector house whose size is the golden ratio? in fact not--the golden ratio isn't really an integer! yet this may take place 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 thought, Hopf algebras, operator algebras, low-dimensional topology (in specific, knot theory), homotopy conception, quantum mechanics and box idea, quantum computation, idea of reasons, and so forth. This ebook offers a scientific advent to this concept and a assessment of its functions. whereas giving an in depth assessment of normal tensor different types, it focuses specially at the concept of finite tensor different types and fusion different types (in specific, braided and modular ones), and discusses the most effects approximately them with proofs. specifically, it exhibits how the most houses of finite-dimensional Hopf algebras might be derived from the idea of tensor different types. Many vital effects are provided as a series of workouts, which makes the publication helpful for college kids and compatible for graduate classes. Many purposes, connections to different parts, extra effects, and references are mentioned on the finish of every bankruptcy.
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