LEADER 04636nam 22007335 450 001 9910300433403321 005 20220415193135.0 010 $a3-319-14301-8 024 7 $a10.1007/978-3-319-14301-9 035 $a(CKB)3710000000337863 035 $a(EBL)1967415 035 $a(OCoLC)900193780 035 $a(SSID)ssj0001424626 035 $a(PQKBManifestationID)11766587 035 $a(PQKBTitleCode)TC0001424626 035 $a(PQKBWorkID)11369599 035 $a(PQKB)11300587 035 $a(DE-He213)978-3-319-14301-9 035 $a(MiAaPQ)EBC1967415 035 $a(PPN)18351937X 035 $a(EXLCZ)993710000000337863 100 $a20150113d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTensor categories and endomorphisms of von Neumann algebras $ewith applications to quantum field theory /$fby Marcel Bischoff, Yasuyuki Kawahigashi, Roberto Longo, Karl-Henning Rehren 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (103 p.) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v3 300 $aDescription based upon print version of record. 311 $a3-319-14300-X 320 $aIncludes bibliographical references at the end of each chapters. 327 $aIntroduction -- Homomorphisms of von Neumann algebras -- Endomorphisms of infinite factors -- Homomorphisms and subfactors -- Non-factorial extensions -- Frobenius algebras, Q-systems and modules -- C* Frobenius algebras -- Q-systems and extensions -- The canonical Q-system -- Modules of Q-systems -- Induced Q-systems and Morita equivalence -- Bimodules -- Tensor product of bimodules -- Q-system calculus -- Reduced Q-systems -- Central decomposition of Q-systems -- Irreducible decomposition of Q-systems -- Intermediate Q-systems -- Q-systems in braided tensor categories -- a-induction -- Mirror Q-systems -- Centre of Q-systems -- Braided product of Q-systems -- The full centre -- Modular tensor categories -- The braided product of two full centres -- Applications in QFT -- Basics of algebraic quantum field theory -- Hard boundaries -- Transparent boundaries -- Further directions -- Conclusions. 330 $aC* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables. The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models. It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system, braided product, centre and full centre of Q-systems) some of which are defined only in the presence of a braiding. The last chapter gives a brief exposition of the relevance of the mathematical structures presented in the main body for applications in Quantum Field Theory (in particular two-dimensional Conformal Field Theory, also with boundaries or defects). 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v3 606 $aQuantum field theory 606 $aString theory 606 $aMathematical physics 606 $aAlgebra 606 $aQuantum Field Theories, String Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19048 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 615 0$aQuantum field theory. 615 0$aString theory. 615 0$aMathematical physics. 615 0$aAlgebra. 615 14$aQuantum Field Theories, String Theory. 615 24$aMathematical Physics. 615 24$aAlgebra. 676 $a515.63 700 $aBischoff$b Marcel$4aut$4http://id.loc.gov/vocabulary/relators/aut$01060170 702 $aKawahigashi$b Yasuyuki$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLongo$b Roberto$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRehren$b Karl-Henning$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300433403321 996 $aTensor Categories and Endomorphisms of von Neumann Algebras$92511524 997 $aUNINA