Abstract
We show that the differential complex Ω B over the braided matrix algebra BM q (N) represents a covariant comodule with respect to the coaction of the Hopf algebra Ω A which is a differential extension of GL q (N). On the other hand, the algebra Ω A is a covariant braided comodule with respect to the coaction of the braided Hopf algebra Ω B . Geometrical aspects of these results are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Faddeev, L. D., Reshetikhin, N. Yu., and Takhtajan, L. A.,Algebra i Analiz 1(1) 178, (1989); English transl,Leningrad Math. J. 1, 193 (1990).
Woronowicz, S. L.,Comm. Math. Phys. 111, 613 (1987).
Kulish, P. P. and Sasaki, R.,Progr. Theoret. Phys. 89, 741 (1993), Kulish, P. P. and Sklyanin, E. K.,J. Phys. A 25, 5963 (1992).
Majid, S.,J. Math. Phys. 32, 3246 (1991).
Majid, S.,J. Math. Phys. 34, 1176 (1993).
Majid, S., Beyond supersymmetry and quantum symmetry (an introduction to braided groups and braided matrices), in M.-L. Ge and H. J. de Vega (eds),Quantum Groups, Integrable Statistical Models and Knot Theory, World Scientific, Singapore, 1993, p. 231.
Faddeev, L. D. and Pyatov, P. N., The differential calculus on quantum linear groups; (1994) (hep-th/9402070), to appear in Berezin's Memorial Volume.
Isaev, A. P. and Pyatov, P. N., Preprint E2-93-416, Dubna (1993) (hepth/9311112).
Sudbery, A.,Math. Proc. Cambridge Philos. Soc. 114, 111 (1993).
Sudbery, A.,Phys. Lett. B 284, 61 (1992), Schirrmacher, A., Remarks on use of R-matrices, in R. Gieleraket al. (eds),Proc. 1st Max Born Symposium, Kluwer Acad. Publ., Dordrecht, 1992, p. 55.
Isaev, A. P. and Pyatov, P. N.,Phys. Lett. A 179, 81 (1993).
Schupp, P., Watts, P., and Zumino, B.,Lett. Math. Phys. 25, 139 (1992).
Isaev, A. P. and Popowicz, Z.,Phys. Lett. B 307, 353 (1993); Isaev, A. P.,J. Math. Phys. 35(12), 6784 (1994).
Brzezinski, T.,Lett. Math. Phys. 27, 287 (1993).
de Azcarraga, J. A., Kulish, P. P., and Rodenas, F.,Lett. Math. Phys. 32, 173 (1994); Kulish, P. P.,Algebra i Analiz 6(2), 195 (1994).
Isaev, A. P. and Vladimirov, A. A.,Lett. Math. Phys. 33 (1995), 297.
Maltsiniotis, G.,Comm. Math. Phys. 151, 275 (1993); Manin, Yu.I.,Teoret. Mat. Fiz. 92, 425 (1992); Baez, J. C.,Lett. Math. Phys. 23, 133 (1991).
Arutyunov, G. E. and Medvedev, P. B., Preprint SMI-11-93, Moscow (1993) (hep-th/9311096); Aref'eva, I., Ya., Arutyunov, G. E., and Medvedev, P. B.,J. Math. Phys. 35(12), 6658 (1994).
Reshetikhin, N. Yu.,Algebra i Analiz 1(2), 169 (1989).
Majid, S.,Lett. Math. Phys. 22, 167 (1991).
Castellani, L.,Phys. Lett. B 292, 93 (1992), Castellani, L., Torino preprints DTFT 74/92 (1992), DTFT 70/93 (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Isaev, A.P. Interrelations between quantum groups and reflection equation (braided) algebras. Lett Math Phys 34, 333–341 (1995). https://doi.org/10.1007/BF00750065
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00750065