000			04621nam a22004813i 4500
001			EBC3114441
003			MiAaPQ
005			20240729124608.0
006			m o d |
007			cr cnu||||||||
008			240724s2012 xx o ||||0 eng d
020			_a9780821891087 _q(electronic bk.)
020			_z9780821869130
035			_a(MiAaPQ)EBC3114441
035			_a(Au-PeEL)EBL3114441
035			_a(CaPaEBR)ebr11041219
035			_a(OCoLC)922965078
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA613.8 -- .S666 2012eb
082	0		_a512/.55
100	1		_aSommerhäuser, Yorck.
245	1	0	_aHopf Algebras and Congruence Subgroups.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2012.
264		4	_c©2012.
300			_a1 online resource (146 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.219
505	0		_aIntro -- 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		_a9.2. 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			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic 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	_aHopf algebras.
650		0	_aModular groups.
655		4	_aElectronic books.
700	1		_aZhu, Yongchang.
776	0	8	_iPrint version: _aSommerhäuser, Yorck _tHopf Algebras and Congruence Subgroups _dProvidence : American Mathematical Society,c2012 _z9780821869130
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114441 _zClick to View
999			_c69936 _d69936