Categories and quantum statistics

Reports on Mathematical Physics

Volumn 38, Issue 2, 1996, Pages 149-174

  Marcinek, Władysław ^a  

^a UNIVERSITY OF WROC AW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030269021     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/0034-4877(96)88948-8     Document Type: Article

References (59)

1. [1] O. W. Greenberg: Phys. Rev. Lett. 64, 705 (1990).
2. [2] Y. S. Wu: J. Math. Phys. 52, 2103 (1984).
3. [3] T. D. Imbo and J. March-Russel: Phys. Lett. B252, 84 (1990).
4. [4] W. Marcinek: Generalized Lie algebras and related topics, Preprint ITP UWr No 691 and 692 (1987).
5. [5] V. V. Lyubashenko: Vectorsymmetries, in Seminar on Supermanifolds, Stockholm University, Report 19, 1 (1987).
6. [6] D. Gurevich: Sov. J. Cont. Math. Anal. 18, 236 (1983).
7. [7] D. Gurevich: Quantum Yang-Baxter equation and a generalization of the formal Lie theory, in Seminar on Supermanifolds, Stockholm University, Report No 19, 33 (1987).
8. [8] D. Gurevich, A. Radul and V. Rubstov: Noncommutative differential geometry and Yang-Baxter equation, I.H.E.S./M/91/88.
9. [9] S. Mac Lane: Categories for Working Mathematician (Graduate Text in Mathematics 5), Springer, Berlin 1971.
10. [10] W. Marcinek: On unital braidings and quantization, Preprint ITP UWr No 847 (1993); Rep. Math. Phys. 34, 325 (1994).
11. [10] W. Marcinek: On unital braidings and quantization, Preprint ITP UWr No 847 (1993); Rep. Math. Phys. 34, 325 (1994).
12. [11] S. Majid: Braided groups, DAMTP/90-42 (1990).
13. [12] S. Majid: Int. J. Mod. Phys. A5, 1 (1990).
14. [13] S. Majid: J. Math. Phys. 34, 2045 (1993).
15. [14] S. Majid: Algebras and Hopf Algebras in Braided Categories, in Advances in Hopf Algebras, Plenum, New York 1993.
16. [15] S. Majid: J. Geom. Phys. 13, 169 (1994).
17. [16] S. Majid: AMS Cont. Math. 134, 219 (1992).
18. [17] Y. I. Manin: Quantum Groups and Noncommutative Geometry, University of Montreal Preprint (1989).
19. [18] D. N. Yetter: Math. Proc. Camb. Phil. Soc. 1108, 263 (1990).
20. [19] P. J. Freyd, D. N. Yetter: Adv. Math. 77, 156 (1989).
21. [20] D. Gurevich: Hecke symmetries and braided Lie algebras, in Spinors, Twistors and Clifford Algebras, eds. Z. Oziewicz et al., Kluwer, Dordrecht 1993, p. 117.
22. [21] D. Gurevich: Alg. Analiz 4, 119 (1990).
23. [22] V. Lyubashenko: J. Pure Appl. Alg. 98, 245 (1995).
24. [23] A. Borowiec, W. Marcinek and Z. Oziewicz: On multigraded differential calculus, in Proceedings of the First Max Born Symposium, ed. R. Gielerak et al., Kluwer, Dordrecht 1992.
25. [24] W. Marcinek: On S-Lie-Cartan pairs, in Spinors, Twistors and Clifford Algebras, eds. Z. Oziewicz et al., Kluwer, Dordrecht 1993, p. 167.
26. [25] W. Marcinek: Rep. Math. Phys. 33, 117 (1993).
27. [26] A. Joyal and R. Street: Braided tensor categories, Preprint.
28. [27] W. Pusz: Rep. Math. Phys. 27, 394 (1989).
29. [28] W. Pusz and S. L. Woronowicz: Rep. Math. Phys. 27, 231 (1989).
30. [29] A. Kempf: Lett. Math. Phys. 26, 1 (1992).
31. [30] A. Kempf: J. Math. Phys. 34, 969 (1993).
32. [31] M. Bozejko and R. Speicher: Interpolation between bosonic and fermionic relations given by generalized Brownian motions, Preprint FSB 132-691, Heildelberg 1992.
33. [32] M. Bozejko, R. Speicher: Math. Ann. 300, 97 (1994).
34. [33] D. B. Fairle and C. K. Zachos: Phys. Lett. B256, 43 (1991).
35. [34] S. P. Vokos: J. Math. Phys. 32, 2979 (1991).
36. [35] M. Arik: The q-difference operator, the quantum hyperplane, Hilbert spaces of analytic functions and q-oscillators, Istanbul Technical University 1991.
37. [36] Ya. Aref'eva and I. V. Volovich: Phys. Lett. B268, 179 (1991).
38. [37] R. J. Finkenlstein: q-Generating functions and the q-oscillators, in Proceedings for the XXI International Conference on Differential Geometric in Theoretical Physics, eds. N. Yang, M. L. Ge and X. W. Zhon, World Scientific, Singapore 1993, p. 201.
39. [38] A. Dimakis and F. Müller-Hoisen: Noncommutative symplectic geometry and quantum mechanics, ibid., p. 214.
40. [39] P. E. T. Jorgensen, L. M. Schmith, and R. F. Werner: Positive representation of general commutation relations allowing Wick ordering, Preprint (1993).
41. [40] W. Marcinek: Noncommutative geometry and the second quantization, in Quantization and Infinite-Dimensional Systems (Proc. XIIth Workshop on Geometric Methods in Physics), eds. J.-P. Antoine et al., Plenum Press, New York, London 1994, p. 21.
42. [41] W. Marcinek: Int. J. Mod. Phys. A10, 1465 (1995).
43. [42] W. Marcinek: On the deformation of commutation relations, in Proceedings of the International Conference in Geometric Methods in Physics, Białowieza, Poland, July 1994.
44. [43] W. Marcinek: On the noncommutative phase space and Poisson structure, University of Kaiserslautern Preprint KL-TH 95/6 (1995).
45. [44] W. Marcinek and R. Rałowski: Particle operators from braided geometry, in Quantum Groups, Formalism and Applications (Proc. XXXth Karpacz Winter School in Theoretical Physics), eds. J. Lukierski et al., PWN, Warszawa 1995, p 149.
46. [45] W. Marcinek and R. Ralowski: On Wick Algebras with Braid Relations, Preprint IFT UWr 876/9 (1994).
47. [46] A. Bruguieres: Commun. Alg. 22, 5817 (1994).
48. [47] S. L. Woronowicz: Commun. Math. Phys. 122, 125 (1989).
49. [48] N. S. Rivaano: Categories Tannakiennes (Lect. Not. Math. 256), Springer, Berlin 1970.
50. [49] J. C. Baez: Lett. Math. Phys. 23, 1333 (1991).
51. [50] P. Glockner: *-Bialgebren in der Quantenstochastik, Heidelberg Dissertation (1989).
52. [51] M. Schurmann: Math. Proc. Camb. Phil. Soc. 107, 149 (1990).
53. [52] P. Glockner: Math. Proc. Camb. Phil. Soc. 109, 571 (1991).
54. [53] R. Ralowski: On deformations of commutation relation algebras, Preprint IFT UWr, No 890 (1995).
55. [54] J. Wess and B. Zumino: Covariant differential calculus on the quantum hyperplane, CERN Preprint 5697/90.
56. [55] B. M. Zupnik: Teor. Mat. Fizika 95, 403 (1993).
57. [56] P. J. M. Bongaarts and H. G. J. Pijls: J. Math. Phys. 35, 959 (1994).
58. [57] P. Vecesernyes: Nucl. Phys. B415, 557 (1994).
59. [58] K. N. Ilinski and V. M. Uzdin: Mod. Phys. Lett. A8, 2657 (1993).