000			nam a22 7a 4500
999			_c28902 _d28902
008			180214b xxu||||| |||| 00| 0 eng d
020			_a9781470437411
082			_a512.57 _bETI
100			_aEtingof, Pavel
245			_aTensor categories
260			_bRhode Island American Mathematical Society, _aProvidence: _c2015
300			_axvi, 343 p. _c26 cm.
365			_aINR _b1225.00
440			_aMathematical surveys and monographs ; volume 205
520			_aIs 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 book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories.
650			_aCategories - Mathematics
650			_aHopf algebras
650			_aAlgebraic topology
650			_aGroup theory
650			_aHomological algebra
700			_aGelaki, Shlomo
700			_aNikshych, Dmitri
700			_aOstrik, Victor
942			_2ddc _cBK