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1
H H Andersen ,
Quantum
groups at roots of ± 1 , Comm. Algebra 24 (1996) 3269
MR1402561
2
H H Andersen ,
J Paradowski , Fusion
categories arising from semisimple Lie algebras , Comm.
Math. Phys. 169 (1995) 563 MR1328736
3
B Bakalov , A
Kirillov Jr. , Lectures on tensor categories and modular
functors , 21, Amer. Math. Soc. (2001) MR1797619
4
P Baumann , On the center of
quantized enveloping algebras , J. Algebra 203 (1998)
244 MR1620662
5
A Beliakova , C
Blanchet , T T Q Lê , Unified quantum invariants
and their refinements for homology 3 –spheres with 2 –torsion , Fund. Math. 201 (2008) 217
MR2457479
6
A Beliakova , I
Bühler , T Le , A unified quantum
SO (3)
invariant for rational homology 3 –spheres , Invent. Math. 185 (2011) 121
MR2810798
7
A Beliakova , Q
Chen , T T Q Le , On the integrality of the
Witten–Reshetikhin–Turaev 3 –manifold invariants , Quantum Topol. 5
(2014) 99 MR3176311
8
A Beliakova , T
Le , On the unification
of quantum 3 –manifold
invariants , from: "Introductory lectures on knot
theory" (editors L H Kauffman, S Lambropoulou, S Jablan,
J H Przytycki), Ser. Knots Everything 46, World Sci.
(2012) 1 MR2885228
9
C Blanchet ,
Hecke
algebras, modular categories and 3 –manifolds quantum invariants ,
Topology 39 (2000) 193 MR1710999
10
A Bruguières ,
Catégories
prémodulaires, modularisations et invariants des variétés de
dimension 3 , Math. Ann. 316
(2000) 215 MR1741269
11
P Caldero , Éléments
ad-finis de certains groupes quantiques , C. R. Acad. Sci.
Paris Sér. I Math. 316 (1993) 327 MR1204298
12
V Chari , A
Pressley , A guide to quantum groups , Cambridge Univ.
Press (1994) MR1300632
13
C Chevalley ,
Invariants of
finite groups generated by reflections , Amer. J. Math.
77 (1955) 778 MR0072877
14
C De Concini ,
V G Kac , C Procesi , Quantum coadjoint
action , J. Amer. Math. Soc. 5 (1992) 151 MR1124981
15
C De Concini , C
Procesi , Quantum groups ,
from: "D–modules, representation theory, and quantum groups"
(editors G Zampieri, A D’Agnolo), Lecture Notes in Math. 1565,
Springer (1993) 31
16
F Deloup , Linking forms,
reciprocity for Gauss sums and invariants of 3 –manifolds , Trans. Amer. Math. Soc.
351 (1999) 1895 MR1603898
17
V G Drinfel’d ,
Quantum groups , from: "Proceedings of the International
Congress of Mathematicians" (editor A M Gleason), Amer.
Math. Soc. (1987) 798 MR934283
18
F Gavarini ,
The quantum
duality principle , Ann. Inst. Fourier (Grenoble) 52
(2002) 809 MR1907388
19
M Goussarov ,
Finite type
invariants and n –equivalence of
3 –manifolds , C. R. Acad.
Sci. Paris Sér. I Math. 329 (1999) 517 MR1715131
20
K Habiro , Claspers and finite type
invariants of links , Geom. Topol. 4 (2000) 1 MR1735632
21
K Habiro , On the quantum
sl 2 invariants of knots and integral
homology spheres , from: "Invariants of knots and
3–manifolds" (editors T Ohtsuki, T Kohno, T Le, J Murakami, J
Roberts, V Turaev), Geom. Topol. Monogr. 4 (2002) 55 MR2002603
22
K Habiro , Cyclotomic
completions of polynomial rings , Publ. Res. Inst. Math.
Sci. 40 (2004) 1127 MR2105705
23
K Habiro , Bottom tangles and
universal invariants , Algebr. Geom. Topol. 6 (2006)
1113 MR2253443
24
K Habiro , Refined Kirby
calculus for integral homology spheres , Geom. Topol. 10
(2006) 1285 MR2255498
25
K Habiro , An integral form
of the quantized enveloping algebra of sl 2 and
its completions , J. Pure Appl. Algebra 211 (2007) 265
MR2333771
26
K Habiro , A unified
Witten–Reshetikhin–Turaev invariant for integral homology
spheres , Invent. Math. 171 (2008) 1 MR2358055
27
M Hennings ,
Invariants
of links and 3 –manifolds obtained
from Hopf algebras , J. London Math. Soc. 54 (1996) 594
MR1413901
28
J Hoste , A formula for Casson’s
invariant , Trans. Amer. Math. Soc. 297 (1986) 547
MR854084
29
J E Humphreys ,
Introduction to Lie
algebras and representation theory , 9, Springer (1978)
MR499562
30
J C Jantzen ,
Lectures on quantum groups , 6, Amer. Math. Soc. (1996)
MR1359532
31
V F R Jones ,
Hecke algebra
representations of braid groups and link polynomials ,
Ann. of Math. 126 (1987) 335 MR908150
32
A Joseph , G
Letzter , Separation of variables for
quantized enveloping algebras , Amer. J. Math. 116
(1994) 127 MR1262429
33
A Joseph , G
Letzter , Rosso’s form and quantized
Kac Moody algebras , Math. Z. 222 (1996) 543 MR1406268
34
M Kashiwara ,
On
crystal bases of the Q –analogue of
universal enveloping algebras , Duke Math. J. 63 (1991)
465 MR1115118
35
C Kassel , Quantum
groups , 155, Springer (1995) MR1321145
36
L H Kauffman ,
Gauss
codes, quantum groups and ribbon Hopf algebras , Rev.
Math. Phys. 5 (1993) 735 MR1253734
37
L H Kauffman ,
D E Radford , Invariants of
3 –manifolds derived from
finite-dimensional Hopf algebras , J. Knot Theory
Ramifications 4 (1995) 131 MR1321293
38
T Kerler , Genealogy
of non-perturbative quantum-invariants of 3 –manifolds : the surgical family , from:
"Geometry and physics" (editors J E Andersen, J Dupont, H
Pedersen, A Swann), Lecture Notes in Pure and Appl. Math. 184,
Dekker (1997) 503 MR1423190
39
R Kirby , A calculus for framed
links in S 3 , Invent. Math. 45 (1978) 35
MR0467753
40
R Kirby , P
Melvin , The
3 –manifold invariants of Witten and
Reshetikhin–Turaev for sl (2 ,C ) ,
Invent. Math. 105 (1991) 473 MR1117149
41
A Klimyk , K
Schmüdgen , Quantum groups and
their representations , Springer (1997) MR1492989
42
T Kohno , T
Takata , Level-rank duality of Witten’s 3 –manifold invariants , from: "Progress in
algebraic combinatorics" (editors E Bannai, A Munemasa), Adv.
Stud. Pure Math. 24, Math. Soc. Japan (1996) 243 MR1414470
43
T Kuriya ,
T T Q Le , T Ohtsuki , The perturbative
invariants of rational homology 3 –spheres can be recovered from the LMO
invariant , J. Topol. 5 (2012) 458 MR2928084
44
R J Lawrence ,
A universal link invariant , from: "The interface of
mathematics and particle physics" (editors D G Quillen,
G B Segal, S T Tsou), Inst. Math. Appl. Conf. Ser.
New Ser. 24, Oxford Univ. Press (1990) 151 MR1103138
45
R J Lawrence ,
Asymptotic
expansions of Witten–Reshetikhin–Turaev invariants for some
simple 3 –manifolds , J.
Math. Phys. 36 (1995) 6106 MR1355900
46
T T Q Le ,
An invariant
of integral homology 3 –spheres
which is universal for all finite type invariants ,
from: "Solitons, geometry, and topology: on the crossroad"
(editors V M Buchstaber, S P Novikov), Amer. Math.
Soc. Transl. Ser. 2 179, Amer. Math. Soc. (1997) 75 MR1437158
47
T T Q Le ,
Integrality and
symmetry of quantum link invariants , Duke Math. J. 102
(2000) 273 MR1749439
48
T T Q Le ,
On
perturbative PSU ( n ) invariants of rational homology 3 –spheres , Topology 39 (2000) 813
MR1760430
49
T T Q Le ,
Quantum
invariants of 3 –manifolds : integrality, splitting, and
perturbative expansion , Topology Appl. 127 (2003) 125
MR1953323
50
T T Q Lê ,
Strong
integrality of quantum invariants of 3 –manifolds , Trans. Amer. Math. Soc.
360 (2008) 2941 MR2379782
51
T T Q Le ,
J Murakami , T Ohtsuki , On a universal
perturbative invariant of 3 –manifolds , Topology 37 (1998) 539
MR1604883
52
G Lusztig , Canonical bases arising
from quantized enveloping algebras, II , Progr. Theoret.
Phys. Suppl. (1990) 175 MR1182165
53
G Lusztig , Quantum groups at roots of
1 , Geom. Dedicata 35 (1990)
89 MR1066560
54
G Lusztig , Introduction to
quantum groups , 110, Birkhäuser (1993) MR1227098
55
V V Lyubashenko ,
Invariants of
3 –manifolds and projective
representations of mapping class groups via quantum groups at
roots of unity , Comm. Math. Phys. 172 (1995) 467
MR1354257
56
I G Macdonald ,
Symmetric functions and orthogonal polynomials , 12,
Amer. Math. Soc. (1998) MR1488699
57
S Majid , Algebras
and Hopf algebras in braided categories , from: "Advances in
Hopf algebras" (editors J Bergen, S Montgomery), Lecture Notes
in Pure and Appl. Math. 158, Dekker (1994) 55 MR1289422
58
S Majid , Foundations of
quantum group theory , Cambridge Univ. Press (1995)
MR1381692
59
Y I Manin ,
Cyclotomy and analytic geometry over 𝔽 1 ,
from: "Quanta of maths" (editors E Blanchard, D Ellwood, M
Khalkhali, M Marcolli, S Popa), Clay Math. Proc. 11, Amer.
Math. Soc. (2010) 385 MR2732059
60
M Marcolli ,
Cyclotomy
and endomotives , p–adic Numbers Ultrametric Anal. Appl.
1 (2009) 217 MR2566053
61
G Masbaum , J D
Roberts , A simple proof of
integrality of quantum invariants at prime roots of
unity , Math. Proc. Cambridge Philos. Soc. 121 (1997)
443 MR1434653
62
G Masbaum , H
Wenzl , Integral modular
categories and integrality of quantum invariants at roots of
unity of prime order , J. Reine Angew. Math. 505 (1998)
209 MR1662260
63
H Murakami ,
Quantum
SO (3) –invariants dominate the SU (2) –invariant of
Casson and Walker , Math. Proc. Cambridge Philos. Soc.
117 (1995) 237 MR1307078
64
T Ohtsuki , Colored ribbon Hopf
algebras and universal invariants of framed links , J.
Knot Theory Ramifications 2 (1993) 211 MR1227011
65
T Ohtsuki , Invariants of
3 –manifolds derived from universal
invariants of framed links , Math. Proc. Cambridge
Philos. Soc. 117 (1995) 259 MR1307080
66
T Ohtsuki , Finite type
invariants of integral homology 3 –spheres , J. Knot Theory Ramifications
5 (1996) 101 MR1373813
67
T Ohtsuki , A polynomial invariant
of rational homology 3 –spheres , Invent. Math. 123 (1996) 241
MR1374199
68
T Ohtsuki , Quantum
invariants : a study of
knots, 3 –manifolds, and their
sets , 29, World Sci. (2002) MR1881401
69
D E Radford ,
Minimal
quasitriangular Hopf algebras , J. Algebra 157 (1993)
285 MR1220770
70
N Y Reshetikhin ,
Quasitriangular Hopf
algebras and invariants of links , Algebra i Analiz 1
(1989) 169 MR1025161
71
N Y Reshetikhin ,
M A Semenov-Tian-Shansky , Quantum
R –matrices and factorization
problems , J. Geom. Phys. 5 (1988) 533 MR1075721
72
N Y Reshetikhin ,
V G Turaev , Ribbon graphs
and their invariants derived from quantum groups , Comm.
Math. Phys. 127 (1990) 1 MR1036112
73
N Reshetikhin ,
V G Turaev , Invariants of 3 –manifolds via link polynomials and quantum
groups , Invent. Math. 103 (1991) 547 MR1091619
74
M Rosso , Analogues
de la forme de Killing et du théorème d’Harish-Chandra pour les
groupes quantiques , Ann. Sci. École Norm. Sup. 23
(1990) 445 MR1055444
75
L Rozansky ,
Witten’s
invariants of rational homology spheres at prime values of
K and trivial connection
contribution , Comm. Math. Phys. 180 (1996) 297 MR1405953
76
L Rozansky ,
On
p –adic properties of the
Witten–Reshetikhin–Turaev invariant , from: "Primes and
knots" (editors T Kohno, M Morishita), Contemp. Math. 416,
Amer. Math. Soc. (2006) 213 MR2276143
77
S F Sawin ,
Invariants
of Spin three-manifolds from Chern–Simons theory and
finite-dimensional Hopf algebras , Adv. Math. 165 (2002)
35 MR1880321
78
S Suzuki , On the universal
sl 2 invariant of ribbon bottom
tangles , Algebr. Geom. Topol. 10 (2010) 1027 MR2629775
79
S Suzuki , On the universal
sl 2 invariant of boundary bottom
tangles , Algebr. Geom. Topol. 12 (2012) 997 MR2928903
80
T Takata , Y
Yokota , The PSU ( N ) invariants of
3 –manifolds are algebraic
integers , J. Knot Theory Ramifications 8 (1999) 521
MR1697388
81
T Tanisaki ,
Killing
forms, Harish-Chandra isomorphisms, and universal R –matrices for quantum algebras , from:
"Infinite analysis, B" (editors A Tsuchiya, T Eguchi, M Jimbo),
Adv. Ser. Math. Phys. 16, World Sci. Publ. (1992) 941 MR1187582
82
V G Turaev ,
Quantum invariants of knots and 3 –manifolds , 18, Walter de Gruyter (1994)
MR1292673
83
A Virelizier ,
Kirby
elements and quantum invariants , Proc. London Math.
Soc. 93 (2006) 474 MR2251160
84
E Witten , Quantum field
theory and the Jones polynomial , Comm. Math. Phys. 121
(1989) 351 MR990772