Abstract
This is an informal overview of versions of quantum algebras which are currently finding applications in physics. Special attention is given to the quantum deformations of SU(2) and illustrations of general principles.
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Work supported by the U.S.Department of Energy, Division of High Energy Physics, Contract W-31-109-ENG-38
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References
L. Alvarez-Gaumé, C. Gomez, and G. Sierra, Phys.Lett. 220B (1989) 142; Nucl.Phys. B319 (1989) 155.
D. Arnaudon and A. Chakrabarti, Ecole Polytechnique preprint, June 1990.
M. Batchelor, L. Mezincescu, R. Nepomechie, and V. Rittenberg, J.Phys. A23 (1990) L141.
D. Bernard and A. Leclair, Phys.Lett. 227B (1989) 417.
L. Biedenharn, J.Phys. A22 (1989) L873; Proceedings of the 1989 Clausthal Workshop, Springer-Verlag, Berlin, 1990; L. Biendenharn and M. Tarlini, Lett.Math.Phys. 20 (1990), in press.
L. Biedenharn and J. Louck, Angular Momentum in Quantum Physics, (Encyclopedia of Mathematics and Its Applications 8), Addison Wesley, 1981.
A. Bracken, H. Gould, and R. Zhang, Mod.Phys.Lett. A5(1990) 831.
N. Burroughs, Comm.Math.Phys. 127 (1990) 109.
D. Caldi, A. Cllodos, Z. Zhu, and A. Barth, Yale preprint YCTP-P13–90, July 1990.
M. Chaichian and D. Ellinas, J.Phys. A23 (1990) L291.
M. Chaichian, D. Ellinas, and P. Kulish, Helsinki preprint, HU-TFT-90–16, March 1990.
M. Chaichian and P. Kulish, Phys.Lett. 234B (1990) 72.
M. Chaichian, P. Kulish, and J. Lukierski, Phys.Lett. 237B (1990) 401.
T. Curtright, Miami preprint TH/1/89, to appear in Physics and Geometry, L-L. Chau and W. Nahm, eds., Plenum, 1990.
T. Curtright, Miami preprint TH/3/90, to appear in the Proceedings of the Argonne Workshop on Quantum Groups, T. Curtright, D. Fairlie, and C. Zachos (eds.), World Scientific, 1990.
T. Curtright and G. Ghandour, Miami preprint TH/8/89.
T. Curtright, G. Ghandour and C. Zachos, Argonne preprint ANL-HEP-PR-90–08, March 1990, to appear in J.Math.Phys.
T. Curtright and C. Zachos, Phys.Lett. 243B (1990) 237.
E. Date, M. Jimbo, K. Miki, and T. Miwa, Kyoto preprint RIMS-703, June 1990.
C. DeConcini and V. Kac, Pisa SNS-math. preprint 75, May 1990.
T. Deguchi, A. Fuji, and K. Ito, Phys.Lett. 238B (1990) 242.
C. Devchand, Freiburg Preprint, to appear in Physics and Geometry, L-L. Chau and W. Nahm, eds., Plenum, 1990.
H. de Vega, Int.J.Mod.Phys. A4 (1989) 2371.
V. Dobrev, Sofia preprint, INRNE-TH-90, August 1990, these proceedings.
V. Drinfeld, Sov.Math.Dokl. 32 (1985) 254; Proc.Int.Cong. Mathematicians, Berkeley 1986, (1987) 798.
L. Faddeev, N. Reshetikhin, and L. Takhtajan, Alg.Anal. 1 (1988) 129; also in Braid Group, Knot Theory and Statistical Mechanics, C. Yang and M. Ge (eds.), World Scientific, 1989.
D. Fairlie, J.Phys. A23 (1990) L183.
D. Fairlie, to appear in the Proceedings of the Argonne Workshop on Quantum Groups, T. Curtright, D. Fairlie, and C. Zachos (eds.), World Scientific, 1990.
D. Fairlie, J. Nuyts, and C. Zachos, Phys.Lett. 202B, 320 (1988).
D. Fairlie and C. Zachos, Phys.Lett. 224B (1989) 101; D. Fairlie, P. Fletcher, and C. Zachos, J.Math.Phys. 31 (1990) 1088.
It. Floreanini, V. Spiridonov, and L. Vinet, Phys.Lett. 242B (1990) 383.
A. Ganchev and V. Petkova, Phys.Lett. 233B (1989) 374.
M-L. Ge, Y-S. Wu, and K. Xue, Stony Brook preprint, ITP-SB-90–02.
M. Gerstenhaber and S. Schack, Proc.Acad.Sci.USA 87 (1990) 478.
J-L. Gervais, Comm.Math.Phys. 130 (1990) 257; Phys. Lett. 243B (1990) 85.
C. Gómez and G. Sierra, Phys.Lett. 240B (1990) 149.
O.W. Greenberg, to appear in the Proceedings of the Argonne Workshop on Quantum Groups, T. Curtright, D. Fairlie, and C. Zachos (eds.), World Scientific, 1990.
B. Gruber and A. Klimyk, Kiev preprint, July 1990 and these proceedings; A. Klimyk, Kiev preprint ITP-90–27E.
E. Guadagnini et al., Phys.Lett. 235B (1990)275.
T. Hayashi, Comm.Math.Phys. 127 (1990) 129.
Bo-Yu Hou, Bo-Yuan Hou, and Z-Q. Ma, Beijing preprints BIHEP-TH-89–7; 8.
H. Itoyama, Phys.Lett. 140A (1989) 391.
H. Itoyama and A. Sevrin, Stony Brook preprint, ITP-SB-90–12, February 1990.
S. Iwao, Prog.Theo.Phys. 83 (1990) 363.
M. Jimbo, Lett.Math.Phys. 10 (1985) 63; 11 (1986) 247; Commun.Math.Phys. 102 (1986) 537.
M. Jimbo, Int.J.Mod.Phys. A4 (1989) 3759.
N. Jing, to appear in Inv.Math.
M. Kashiwara, Kyoto preprint RIMS-676, December 1989.
L. Kauffman, Int.J.Mod.Phys. A5 (1990) 93.
A. Kirillov and N. Reshetikhin, in Infinite Dimensional Lie Algebras and Groups, Marseille 1988 Meeting, V. Kac (ed.), World Scientific, 1989.
I. Koh and Z-Q. Ma, Phys.Lett. 234B (1990) 480.
T. Koornwinder, Proc. Kon. Ned. Akad. Wetensch. A92 (1989) 97; H. Koelink and T. Koornwinder, ibid. A92 (1989) 443.
Y. Kosmann-Schwarzbach, Mod.Phys.Lett. A5 (1990) 981.
P. Kulish and E. Damashinsky, J.Phys. A23 (1990) L415.
P. Kulish and N. Reshetikhin, J.Sov.Math. 23 (1983) 2435.
P. Kulish and N. Reshetikhin, Lett.Math.Phys. 18 (1989) 143.
G. Lusztig, Adv.Math. 70 (1988) 237.
G. Lusztig, Cont.Math. 82 (1989) 59.
Z-Q. Ma, Beijing Preprint, BIHEP-TH-90–14, May 1990.
A. Macfarlane, J.Phys. A22 (1989) 4581.
S. Majid, Int.J.Mod.Phys. A5 (1990) 1.
S. Majid and Y. Soibelman, Cambridge preprint, DAMTP/90–12, July 1990.
Y. Manin, Quantum Groups and Non-Commutative Geometry, Cent.R.Math.-1561, Univ. Montréal, 1988.
Y. Manin, Comm.Math.Phys. 123 (1989) 163.
T. Masuda et al., Lett.Math.Phys. 19 (1990) 187; 195.
L. Mezincescu and R. Nepomechie, Phys.Lett. 246B (1990) 412.
G. Moore and N. Reshetikhin, Nucl.Phys B328 (1989) 557.
T. Nakashima, Kyoto preprint RIMS-682, February 1990.
F. Narganes-Quijano, Brussels preprint, ULB-TH-90/01, Mach 1990.
Y. Ng, J.Phys. A23 (1990) 1023.
M. Nomura, J.Math.Phys. 30 (1989) 2397; J.Phys.Soc.Jap. 58 (1989) 2694; ibid. 59 (1990) 439; 1954; 2345.
A. Odesskii, Funct.AnaLAppl. 20 (1986) 152.
V. Pasquier, Comm.Math.Phys. 118 (1988) 355.
V. Pasquier and H. Saleur, Nucl.Phys. B330 (1990) 523.
A. Polychronakos Florida preprint, UFTP-89–23, November 1989.
A. Polychronakos Florida preprint, UFIFT-HEP-90–14, 1990, to appear in the Proceedings of the Argonne Workshop on Quantum Groups, T. Curtright, D. Fairlie, and C. Zachos (eds.), World Scientific, 1990.
P. Raychev, R. Roussev, and Yu. Smirnov, J.Phys. G16 (1990) L137.
N. Reshetikhin, Steklov preprint LOMI-E-4–87, E-17–87 (1988).
N. Reshetikhin and M. Semenov-Tian-Shansky, Lett.Math.Phys. 19 (1990) 133.
N. Reshetikhin and F. Smirnov, Comm.Math.Phys. 131 (1990) 157.
P. Roche and D. Arnaudon, Lett.Math.Phys. 17 (1989) 295.
L. Romans, in Strings ‘89, R. Arnowitt et al. (eds.), World Scientific, 1990, contains a substantial bibliography.
M. Rosso, Comm.Math.Phys. 117 (1988) 581.
M. Rosso, C.R.Acad.Sc.Paris, 304 (1987) 323.
H. Ruegg, J.Math.Phys. 31 (1990) 1085.
H. Saleur, Number Theory and Physics, p. 68, Springer Proceedings in Physics 47, J. Luck et al. (eds.), Springer Verlag, 1990.
H. Saleur, Nucl.Phys. B336 (1990) 363.
H. Saleur and D. Altschiiler, SphT/90–041, June 1990.
G. Siopsis, Texas A&M preprint, CTP-TAMU-33/90, March 1990.
E. Sklyanin, Funct.Anal.Appl. 16 (1982) 263.
E. Sklyanin, Uspekhi.Mat.Nauk. 40 (1985) 214.
A. Sudbery, to appear in the Proceedings of the Argonne Workshop on Quantum Groups, T. Curtright, D. Fairlie, and C. Zachos (eds.), World Scientific, 1990.
C-P. Sun and H-C. Fu, J.Phys. A22 (1989) L983.
K. Ueno, T. Takebayashi, and Y. Shibukawa, Lett.Math.Phys. 18 (1989) 215.
L. Vaksman, Sov.Math.Dokl. 39 (1989) 467.
L. Vaksman and Y. Soibelman, Funct.Anal.Appl. 22 (1988) 170.
S. Vokos, B. Zumino, and J. Wess, Berkeley preprint UCH-PTH-89/25.
Wess and Zumino, preprint CERN-TH-5697/90, April 1990.
E. Witten, Nucl.Phys. B330 (1990) 285.
S. Woronowicz, Publ. RIMS-Kyoto 23 (1987) 117; Comm.Math.Phys. 111 (1987) 613; 122 (1989) 125; 130 (1990) 381.
C. Zachos, ANL-HEP-CP-90–43, July 1990, to appear in the Proceedings of the Argonne Workshop on Quantum Groups, T. Curtright, D. Fairlie, and C. Zachos (eds.), World Scientific, 1990.
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Zachos, C. (1991). Paradigms of Quantum Algebras. In: Gruber, B., Biedenharn, L.C., Doebner, H.D. (eds) Symmetries in Science V. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3696-3_29
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