Remarks on quantum integration

Communications in Mathematical Physics

Volumn 184, Issue 1, 1997, Pages 1-25

  Chryssomalakos, Chryssomalis ^a  

^a Lab de Phys Theor ENSLAPP   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031546434     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050050     Document Type: Article

References (24)

1. Abe, E.: Hopf Algebras, Cambridge: Cambridge Univ. Press, 1980
2. Chryssomalakos, C., Schupp, P., Watts, P.: The Role of the Canonical Element in the Quantized Algebra of Differential Operators A⋊U. Preprint LBL-33274, UCB-PTH-92/42
3. Chryssomalakos, C., Zumino, B.: Translations, Integrals And Fourier Transforms In The Quantum Plane. In: Ali, A., Ellis, J., Randjbar-Daemi, S. (eds.) Salamfestschrift. Proceedings of the "Conference On Highlights Of Particle And Condensed Matter Physics", ICTP, Trieste, Italy 1993
4. Chryssomalakos, C., Schupp, S., Zumino, B.: Induced Extended Calculus On The Quantum Plane. Alg. i Anal. 6, 252 (1994)
5. Chu, C.S., Zumino, B.: Realization of Vector Fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces. Preprint LBL-36746, UCB-PTH-95/04, q-alg/9502005
6. Chu, C.S., Ho, P.M., Zumino, B.: The Quantum 2-Sphere as a Complex Quantum Manifold. To appear in Z. Phys.
7. Drinfel'd, V.G.: Quantum Groups. In Gleason, A. (ed.) Proceedings of the ICM, Providence, Rhode Island AMS, 1987
8. q and its Hilbert Space Structure. Int. J. Mod. Phys. A8, 4679-4729 (1993)
9. Faddeev, L.D., Reshetikhin, N.Yu., Takhtadzhyan, L.A.: Quantization of Lie Groups and Lie Algebras. Leningrad Math. J. 1, 193-225 (1990)
10. Kempf, A., Majid, S.: Algebraic q-integration and Fourier Theory on Quantum and Braided Spaces. Preprint DAMTP/94-7
11. Larson, R.G., Radford, D.E.: Semisimple Cosemisimple Hopf Algebras. Am. J. Math. 109, 187 (1988)
12. Larson, R.G., Sweedler, M.E.: An Associative Orthogonal Bilinear Form for Hopf Algebras. Am. J. Math. 91, 75-94 (1969)
13. Lyubashenko, V.: Tangles and Hopf Algebras In Braided Categories. J. Pur. Appl. Alg 98, 245-278 (1995)
14. Lyubashenko, V.: Modular Transformations for Tensor Categories. J. Pur. Appl. Alg. 98, 279-327 (1995)
15. Majid, S.: Quasitriangular Hopf Algebras and Yang-Baxter Equations. Int. J. Mod. Phys. A5, 1-91 (1990)
16. Majid, S.: Braided Momentum in the q-Poincare Group. J. Math. Phys. 34, 2045-2058 (1993)
17. Majid, S.: Beyond Supersymmetry and Quantum Symmetry (An introduction to braided groups and braided matrices). In: Ge, M.L., de Vega, H.J. (eds.), Quantum Groups, Integrable Statistical Models and Knot Theory. Singapore: World Sci., 1993, pp. 231-282
18. Majid, S.: Lie Algebras And Braided Geometry. Adv. Appl. Cliff. Alg. 4, (S1), 61-77 (1994)
19. Radford, D.E.: The Trace Function And Hopf Algebras. Preprint
20. Radford, D.E.: The Order of the Antipode of a Finite Dimensional Hopf Algebra is Finite. Am. J. Math. 98, (2), 333-355 (1973)
21. Steinacker, H.: Integration on Quantum Euclidean Space and Sphere in N Dimensions. Preprint LBL-37431, UCB-PTH-95/21; q-alg 9506020
22. Sweedler, M.E.: Hopf Algebras. New York: Benjamin, 1969
23. Van Daele, A.: The Haar Measure On Finite Quantum Groups. Preprint K. U. Leuven, November 1992
24. Van Daele, A.: Private communication