LEADER 04494nam 2200613 450 001 9910817266103321 005 20170822144326.0 010 $a1-4704-0556-3 035 $a(CKB)3360000000465126 035 $a(EBL)3114165 035 $a(SSID)ssj0000889092 035 $a(PQKBManifestationID)11521343 035 $a(PQKBTitleCode)TC0000889092 035 $a(PQKBWorkID)10876422 035 $a(PQKB)10346611 035 $a(MiAaPQ)EBC3114165 035 $a(RPAM)15734696 035 $a(PPN)19541831X 035 $a(EXLCZ)993360000000465126 100 $a20150416h20092009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNoncommutative curves of genus zero $erelated to finite dimensional algebras /$fDirk Kussin 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2009. 210 4$dİ2009 215 $a1 online resource (146 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 201, Number 942 300 $a"Volume 201, Number 942 (first of 5 numbers)." 311 $a0-8218-4400-8 320 $aIncludes bibliographical references and index. 327 $a""Contents""; ""Introduction""; ""Chapter 0. Background""; ""0.1. Notation""; ""0.2. One-parameter families, generic modules and tameness""; ""0.3. Canonical algebras and exceptional curves""; ""0.4. Tubular shifts""; ""0.5. Tame bimodules and homogeneous exceptional curves""; ""0.6. Rational points""; ""Part 1. The homogeneous case""; ""Chapter 1. Graded factoriality""; ""1.1. Efficient automorphisms""; ""1.2. Prime ideals and universal extensions""; ""1.3. Prime ideals as annihilators""; ""1.4. Noetherianness""; ""1.5. Prime ideals of height one are principal"" 327 $a""1.6. Unique factorization""""1.7. Examples of graded factorial domains""; ""The non-simple bimodule case""; ""The quaternion case""; ""The square roots case""; ""Chapter 2. Global and local structure of the sheaf category""; ""2.1. Serre's theorem""; ""2.2. Localization at prime ideals""; ""2.3. Noncommutativity and the multiplicities""; ""2.4. Localizing with respect to the powers of a prime element""; ""2.5. Zariski topology and sheafification""; ""Chapter 3. Tubular shifts and prime elements""; ""3.1. Central prime elements""; ""3.2. Non-central prime elements and ghosts"" 327 $a""Chapter 4. Commutativity and multiplicity freeness""""4.1. Finiteness over the centre""; ""4.2. Commutativity of the coordinate algebra""; ""4.3. Commutativity of the function field""; ""Chapter 5. Automorphism groups""; ""5.1. The automorphism group of a homogeneous curve""; ""5.2. The structure of Aut(H)""; ""5.3. The twisted polynomial case""; ""5.4. On the Auslander-Reiten translation as functor""; ""5.5. The quaternion case""; ""5.6. The homogeneous curves over the real numbers""; ""5.7. Homogeneous curves with finite automorphism group""; ""Part 2. The weighted case"" 327 $a""Chapter 6. Insertion of weights""""6.1. p-cycles""; ""6.2. Insertion of weights into central primes""; ""6.3. Automorphism groups for weighted curves""; ""Chapter 7. Exceptional objects""; ""7.1. Transitivity of the braid group action""; ""7.2. Exceptional objects and graded factoriality""; ""Chapter 8. Tubular exceptional curves""; ""8.1. Slope categories and the rational helix""; ""8.2. The index of a tubular exceptional curve""; ""8.3. A tubular curve of index three""; ""8.4. A related tubular curve of index two""; ""8.5. Line bundles which are not exceptional"" 327 $a""Appendix A. Automorphism groups over the real numbers""""A.1. Tables for the domestic and tubular cases""; ""Appendix B. The tubular symbols""; ""Bibliography""; ""Index""; ""A""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 201, Number 942. 606 $aCurves, Algebraic 606 $aRepresentations of rings (Algebra) 606 $aNoncommutative algebras 615 0$aCurves, Algebraic. 615 0$aRepresentations of rings (Algebra) 615 0$aNoncommutative algebras. 676 $a516.3/52 700 $aKussin$b Dirk$f1967-$01671647 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910817266103321 996 $aNoncommutative curves of genus zero$94034367 997 $aUNINA