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.
Read Online or Download Tensor Categories (Mathematical Surveys and Monographs) PDF
Similar Algebraic Geometry books
This paintings attracts jointly rules from algebraic topology, sensible research and geometry. it's a instrument - a way of conveying details between those 3 topics - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this publication is to acquaint the reader with the basic rules of analytic K-homology and enhance a few of its functions.
First textbook-level account of easy examples and strategies during this region. compatible for self-study through a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yankee Mathematical Society, in addition to a winning Springer writer.
"It provides a delicate portrait of an exceptional person. It describes properly and intelligibly on a nontechnical point the area of mathematical rules within which Hilbert created his masterpieces. And it illuminates the heritage of German social historical past opposed to which the drama of Hilberts lifestyles was once performed.
From the preface of the writer: ". .. i've got divided this paintings into books; within the first of those i've got constrained myself to these concerns bearing on natural research. within the moment ebook i've got defined these factor which has to be identified from geometry, considering research is commonly built in this sort of method that its software to geometry is proven.
Extra resources for Tensor Categories (Mathematical Surveys and Monographs)