It is shown that the algebra 𝒰p,q dual to GLp,q(2,C) is isomorphic to U(pq)1/2(sl(2,C)) ⊗ 𝒵 as a commutation algebra, where 𝒵 is a subalgebra central in 𝒰p,q. The subalgebra 𝒵 is a Hopf subalgebra of 𝒰p,q, while the commutation subalgebra U(pq)1/2(sl(2,C)) is not a Hopf subalgebra.

1.
P. P.
Kulish
and
N. Yu.
Reshetikhin
,
Zap. Nauch. Semin.
LOMI
101
,
101
(
1981
) (in Russian);
English translation:
P. P.
Kulish
and
N. Yu.
Reshetikhin
,
J. Sov. Math.
23
,
2435
(
1983
).
2.
P. P.
Kulish
,
N. Yu.
Reshetikhin
, and
E. K.
Sklyanin
,
Lett. Math. Phys.
5
,
393
(
1981
).
3.
P. P.
Kulish
and
E. K.
Sklyanin
,
Lect. Notes Phys.
151
,
61
(
1982
).
4.
E. K.
Sklyanin
,
Funkts. Anal. Prilozh.
16
,
27
(
1982
) (in Russian);
English translation:
E. K.
Sklyanin
,
Funct. Anal. Appl.
16
,
263
(
1982
);
E. K.
Sklyanin
,
Funkts. Anal. Prilozh.
17
,
34
(
1983
) (in Russian);
English translation:
E. K.
Sklyanin
,
Funct. Anal. Appl.
17
,
274
(
1983
).
5.
L. D. Faddeev, Integrable models in 1+1 dimensional quantum field theory, in Les Houches Lectures 1982 (Elsevier, Amsterdam, 1984).
6.
E. K.
Sklyanin
,
Uspekhi Mat. Nauk
40
,
214
(
1985
) (in Russian).
7.
V. G.
Drinfeld
,
Dokl. Akad. Nauk SSSR
283
,
1060
(
1985
) (in Russian);
English translation:
V. G.
Drinfeld
,
Sov. Math. Dokl.
32
,
254
(
1985
).
8.
M.
Jimvo
,
Lett. Math. Phys.
10
,
63
(
1985
).
9.
M.
Jimbo
,
Lett. Math. Phys.
11
,
247
(
1986
).
10.
V. G. Drinfeld, in Proceedings ICM (Berkeley, 1986) Vol. 1 (Academic, New York, 1987), pp. 798–820.
11.
L. D. Faddeev, N. Yu. Reshetikhin, and L. A. Takhtajan, LOMI Leningrad preprint E-14-87 (1987) and in Algebraic Analysis, Vol. 1 (Academic, New York, 1988), pp. 129–139;
expanded version:
Alg. Anal.
1
,
178
(
1989
) (in Russian);
English translation:
Leningrad Math. J.
1
,
193
(
1990
).
12.
Yu. I.
Manin
,
Ann. Inst. Fourier
37
,
191
(
1987
);
Montreal University preprint, CRM-1561 (1988).
13.
Yu. I.
Manin
,
Coram. Math. Phys.
123
,
163
(
1989
).
14.
S. L.
Woronowicz
,
Comm. Math. Phys.
111
,
613
(
1987
);
S. L.
Woronowicz
,
Publ. RIMS, Kyoto Univ.
,
23
,
117
(
1987
).
15.
S. L.
Woronowicz
,
Comm. Math. Phys.
122
,
125
(
1989
).
16.
P. P.
Kulish
,
Zapiski Nauch. Semin.
LOMI
180
,
89
(
1990
) (in Russian).
17.
A.
Sudbery
,
J. Phys. A: Math. Gen.
23
,
L697
(
1990
).
18.
E. E.
Demidov
,
Yu. I.
Manin
,
E. E.
Mukhin
, and
D. V.
Zhdanovich
,
Prog. Theor. Phys. Suppl.
102
,
203
(
1990
).
19.
A.
Schirrmacher
,
J.
Wess
, and
B.
Zumino
,
Z. Phys.
C49
,
317
(
1991
).
20.
O.
Ogievetsky
and
J.
Wess
,
Z. Phys. C
50
,
123
(
1991
).
21.
N. Yu.
Reshetikhin
,
Lett. Math. Phys.
20
,
331
(
1990
).
22.
A.
Schirrmacher
,
Z. Phys. C
50
,
321
(
1991
).
23.
D. B.
Fairlie
and
C. K.
Zachos
,
Phys. Lett.
256B
,
43
(
1991
).
24.
M. Takeuchi, Inst. of Math. preprint, Univ. Tsukuba (1990).
25.
H. Ewen, O. Ogievetsky, and J. Wess, Max Planck Institut for Physics preprint MPI-PAE/PTh 18/91 (1991).
26.
N.
Burroughs
,
Comm. Math. Phys.
127
,
109
(
1990
);
N.
Burroughs
,
Comm. Math. Phys.
133
,
91
(
1990
).
27.
T. H. Koornwinder, Orthogonal Polynomials: Theory and Practice, NATO ASI Series C, Vol. 294 (Kluwer, Dordrecht, 1990), pp. 257–292.
28.
T.
Masuda
,
K.
Mimachi
,
Y.
Nakagami
,
M.
Noumi
, and
K.
Ueno
,
C. R. Acad. Sci. Paris Ser. I
307
,
559
(
1988
).
29.
L. L.
Vaksman
and
Ya. S.
Soibelman
,
Funkts. Anal. Prilozh.
22
, (
3
)
1
(
1988
);
English translation:
L. L.
Vaksman
and
Ya. S.
Soibelman
,
Funct. Anal. Appl.
22
,
170
(
1988
).
30.
A. Sudbery, Proceedings of the Workshop on Quantum Groups, Argonne National Lab (1990), edited by T. Curtright, D. Fairlie, and C. Zachos (World Scientific, Singapore, 1991).
31.
M.
Rosso
,
Comm. Math. Phys.
124
,
307
(
1989
).
32.
E. Abe, Hopf Agebras, Cambridge Tracts in Math., N 74 (Cambridge University, Cambridge, 1980).
33.
S.
Majid
,
Int. J. Mod. Phys. A
5
,
1
(
1990
).
34.
L. D.
Faddeev
and
L. A.
Takhtajan
, Proceedings of a seminar series held at DAPHE & LPTHE, Univ. Pierre et Marie Curie (Paris, 1984–1985),
Lect. Notes Phys.
246
,
166
(
1986
).
35.
E.
Corrigan
,
D. B.
Fairlie
,
P.
Fletcher
and
R.
Sasaki
,
J. Math. Phys.
31
,
776
(
1990
).
36.
J.
Wess
and
B.
Zumino
,
Nucl. Phys. (Proc. Suppl.) B
18
,
302
(
1990
).
This content is only available via PDF.
You do not currently have access to this content.