LEADER 04763nam 2200613 450 001 9910827428103321 005 20170822144504.0 010 $a0-8218-9108-1 035 $a(CKB)3360000000464088 035 $a(EBL)3114441 035 $a(SSID)ssj0000888991 035 $a(PQKBManifestationID)11453160 035 $a(PQKBTitleCode)TC0000888991 035 $a(PQKBWorkID)10875998 035 $a(PQKB)10756585 035 $a(MiAaPQ)EBC3114441 035 $a(RPAM)17318775 035 $a(PPN)195419170 035 $a(EXLCZ)993360000000464088 100 $a20150416h20122012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHopf algebras and congruence subgroups /$fYorck Sommerha?user, Yongchang Zhu 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2012. 210 4$dİ2012 215 $a1 online resource (134 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 219, Number 1028 300 $a"September 2012 , Volume 219, Number 1028 (first of 5 numbers)." 311 $a0-8218-6913-2 320 $aIncludes bibliographical references and index. 327 $a""Contents""; ""Abstract""; ""Introduction""; ""Chapter 1. The Modular Group""; ""1.1. Generators and relations""; ""1.2. Congruence subgroups""; ""1.3. Orbits and congruence relations""; ""1.4. Presentations of the reduced modular group""; ""Chapter 2. Quasitriangular Hopf Algebras""; ""2.1. Quasitriangular Hopf algebras""; ""2.2. The Drinfela???d double construction""; ""2.3. Integrals of the Drinfela???d double""; ""2.4. Twisting""; ""Chapter 3. Factorizable Hopf Algebras""; ""3.1. Doubles of quasitriangular Hopf algebras""; ""3.2. Factorizable Hopf algebras"" 327 $a""3.3. The coproduct of the evaluation form""""3.4. The double and the tensor product""; ""3.5. Integrals of factorizable Hopf algebras""; ""Chapter 4. The Action of the Modular Group""; ""4.1. The role of the integral""; ""4.2. The inverse of \ ""; ""4.3. Ribbon elements""; ""4.4. The linearity of the action""; ""4.5. Integrals, ribbon elements, and the double""; ""4.6. The modular group and the double""; ""Chapter 5. The Semisimple Case""; ""5.1. The character ring""; ""5.2. The Verlinde matrix""; ""5.3. Matrix identities""; ""5.4. A comparison""; ""5.5. The exponent"" 327 $a""5.6. Radforda???s example""""Chapter 6. The Case of the Drinfela???d Double""; ""6.1. The role of the evaluation form""; ""6.2. The new maps""; ""6.3. The first relation""; ""6.4. The second approach to the action of the modular group""; ""6.5. Matrix representations of the new maps""; ""Chapter 7. Induced Modules""; ""7.1. Induction""; ""7.2. Induction and duality""; ""7.3. The relation with the center construction""; ""7.4. The relation of the coherence properties""; ""7.5. Adjoint functors""; ""7.6. More coherence properties""; ""Chapter 8. Equivariant Frobenius-Schur Indicators"" 327 $a""8.1. Equivariant Frobenius-Schur indicators""""8.2. Indicators and duality""; ""8.3. The equivariance theorem""; ""8.4. The orbit theorem""; ""Chapter 9. Two Congruence Subgroup Theorems""; ""9.1. The action on the character ring""; ""9.2. Induction and multiplicities""; ""9.3. The congruence subgroup theorem for the Drinfela???d double""; ""9.4. The projective congruence subgroup theorem""; ""Chapter 10. The Action of the Galois Group""; ""10.1. The Galois group and the character ring""; ""10.2. The semilinear actions""; ""10.3. The action on the center"" 327 $a""10.4. Representations of the Drinfela???d double""""10.5. The equivariance of the isomorphism""; ""Chapter 11. Galois Groups and Indicators""; ""11.1. A digression on Frobenius algebras""; ""11.2. The invariance of the induced trivial module""; ""11.3. The action and the indicators""; ""11.4. Diagonal matrices""; ""11.5. The Galois group and the modular group""; ""Chapter 12. Galois Groups and Congruence Subgroups""; ""12.1. The Hopf symbol""; ""12.2. Properties of the Hopf symbol""; ""12.3. The Hopf symbol and the Jacobi symbol""; ""12.4. The linear congruence subgroup theorem""; ""Notes"" 327 $a""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 219, Number 1028. 606 $aHopf algebras 606 $aModular groups 615 0$aHopf algebras. 615 0$aModular groups. 676 $a512/.55 700 $aSommerha?user$b Yorck$f1966-$067460 702 $aZhu$b Yongchang 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827428103321 996 $aHopf algebras and congruence subgroups$93964291 997 $aUNINA LEADER 03424nam 22007095 450 001 9910743342203321 005 20251229075131.0 010 $a981-16-7818-9 010 $a981-16-7817-0 010 $a981-16-7818-9 024 7 $a10.1007/978-981-16-7818-9 035 $a(MiAaPQ)EBC6882496 035 $a(Au-PeEL)EBL6882496 035 $a(CKB)21069312500041 035 $a(PPN)260828076 035 $a(BIP)83139637 035 $a(BIP)81903193 035 $a(DE-He213)978-981-16-7818-9 035 $a(EXLCZ)9921069312500041 100 $a20220202d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAchieving $5 Trillion Economy of India $eProceedings of 11th Annual International Research Conference of Symbiosis Institute of Management Studies /$fedited by Arti Chandani, Rajiv Divekar, J. K. Nayak 205 $a1st ed. 2022. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2022. 215 $a1 online resource (385 pages) 225 1 $aSpringer Proceedings in Business and Economics,$x2198-7254 311 08$aPrint version: Chandani, Arti Achieving Trillion Economy of India Singapore : Springer Singapore Pte. Limited,c2022 9789811678172 330 $aThe contents of this volume focuses on the economic issues such as income inequality, foreign direct investment, world income classification, business issues such as customer churn analysis, internal branding, human resources issues among others. The papers were presented during the 11th Annual Research Conference of Symbiosis Institute of Management Studies (SIMSARC2020). The book also focuses on the information technology and its application for the business in the form of social media, role of artificial intelligence etc. The contents of the volume are highly relevant, consisting of recent data and results, and based on strong research and statistical analysis. They widely cover the business, society and environmental issues faced in the present times, and the challenges faced by India to reach its goal of a trillion dollar economy. The papers not only discuss the issues but also come up with research based solutions and will be of interest to scholars, corporates, policy makers, and academics alike. 410 0$aSpringer Proceedings in Business and Economics,$x2198-7254 606 $aStrategic planning 606 $aLeadership 606 $aEconomic development 606 $aBusiness information services 606 $aInternational trade 606 $aBusiness Strategy and Leadership 606 $aEconomic Development, Innovation and Growth 606 $aIT in Business 606 $aInternational Trade 615 0$aStrategic planning. 615 0$aLeadership. 615 0$aEconomic development. 615 0$aBusiness information services. 615 0$aInternational trade. 615 14$aBusiness Strategy and Leadership. 615 24$aEconomic Development, Innovation and Growth. 615 24$aIT in Business. 615 24$aInternational Trade. 676 $a994.230049915 702 $aDivekar$b Rajiv 702 $aNayak$b J. K. 702 $aChandani$b Arti 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910743342203321 996 $aAchieving$93559939 997 $aUNINA