Hopf Algebras and Congruence Subgroups. (Record no. 69936)
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| fixed length control field | 04621nam a22004813i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC3114441 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729124608.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2012 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780821891087 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780821869130 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC3114441 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL3114441 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11041219 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)922965078 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA613.8 -- .S666 2012eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512/.55 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Sommerhäuser, Yorck. |
| 245 10 - TITLE STATEMENT | |
| Title | Hopf Algebras and Congruence Subgroups. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2012. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2012. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (146 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society ; |
| Volume/sequential designation | v.219 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Intro -- 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 Drinfel'd double construction -- 2.3. Integrals of the Drinfel'd double -- 2.4. Twisting -- Chapter 3. Factorizable Hopf Algebras -- 3.1. Doubles of quasitriangular Hopf algebras -- 3.2. Factorizable Hopf algebras -- 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 -- 5.6. Radford's example -- Chapter 6. The Case of the Drinfel'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 -- 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. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 9.2. Induction and multiplicities -- 9.3. The congruence subgroup theorem for the Drinfel'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 -- 10.4. Representations of the Drinfel'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 -- Bibliography -- Subject Index -- Symbol Index. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Hopf algebras. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Modular groups. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Zhu, Yongchang. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Sommerhäuser, Yorck |
| Title | Hopf Algebras and Congruence Subgroups |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2012 |
| International Standard Book Number | 9780821869130 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114441">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114441</a> |
| Public note | Click to View |
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